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Part I Stability Analysis and Control Design |
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Necessary Stability Conditions for One Delay Systems: A Lyapunov Matrix Approach |
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3 | (14) |
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3 | (2) |
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5 | (4) |
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2.1 Theoretical Framework |
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5 | (2) |
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7 | (2) |
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9 | (3) |
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4 Illustrative Example and Additional Considerations |
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12 | (3) |
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15 | (2) |
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16 | (1) |
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Control of Linear Delay Systems: An Approach without Explicit Predictions |
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17 | (14) |
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17 | (2) |
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2 Controllability Properties |
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19 | (2) |
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3 Remarks on Modules over the Ring K[ δ] |
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21 | (1) |
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4 Prediction-Free Control |
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22 | (2) |
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4.1 Conditions in the Commensurate Case |
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22 | (1) |
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4.2 Conditions in the Incommensurate Case |
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23 | (1) |
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23 | (1) |
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5 Example: A Heat Accumulator |
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24 | (7) |
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5.1 Control via the Jacket Temperature T0 |
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25 | (2) |
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5.2 Control via the Inlet Temperature Tin |
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27 | (1) |
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28 | (1) |
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29 | (2) |
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New Integral Inequality and Its Application to Time-Delay Systems |
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31 | (14) |
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31 | (2) |
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33 | (1) |
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33 | (1) |
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2.2 Different Wirtinger Inequalities |
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33 | (1) |
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3 Application of the Wirtinger's Inequalities |
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34 | (3) |
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4 Appropriate Inequalities for Robust Stability Analysis |
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37 | (1) |
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5 Application to the Stability Analysis of Time-Delay Systems |
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38 | (5) |
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5.1 Systems with Constant and Known Delay |
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39 | (1) |
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5.2 Systems with Constant and Unknown Delay: Delay Range Stability |
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40 | (1) |
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41 | (2) |
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43 | (2) |
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43 | (2) |
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A Matrix Technique for Robust Controller Design for Discrete-Time Time-Delayed Systems |
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45 | (12) |
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45 | (2) |
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47 | (1) |
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3 Robust Stability Analysis |
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48 | (4) |
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4 Dominant Pole Assignment |
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52 | (1) |
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52 | (2) |
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6 Conclusion and Discussion |
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54 | (3) |
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55 | (2) |
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Dominant Trio of Poles Assignment in Delayed PID Control Loop |
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57 | (14) |
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57 | (2) |
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2 Selecting the Candidate Group of Dominant Poles |
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59 | (1) |
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3 Three Pole Dominant Placement in Delayed PID Feedback Loop |
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60 | (3) |
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3.1 Ultimate Frequency Assessment |
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62 | (1) |
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4 Argument Increment Based Check to Prove the Dominance |
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63 | (1) |
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5 Relative Damping Optimization in the PID Parameter Setting |
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64 | (4) |
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65 | (1) |
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5.2 Example 1 - Controlling Second Order System |
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65 | (2) |
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5.3 Example 2 - Controlling Third Order System |
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67 | (1) |
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68 | (3) |
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69 | (2) |
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Stability of Systems with State Delay Subjected to Digital Control |
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71 | (16) |
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71 | (2) |
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73 | (6) |
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73 | (4) |
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77 | (2) |
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3 Example: The Delayed Oscillator |
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79 | (2) |
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4 Example: Application to Turning Processes |
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81 | (1) |
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82 | (5) |
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83 | (4) |
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Part II Networks and Graphs |
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Control Design for Teleoperation over Unreliable Networks: A Predictor-Based Approach |
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87 | (14) |
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87 | (2) |
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2 A Delay Formulation for Teleoperation Problems |
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89 | (1) |
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3 Force-Reflecting Emulator Control Scheme |
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90 | (9) |
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3.1 System Description and Problem Formulation |
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90 | (2) |
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3.2 Problem 1: Local Controller Design |
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92 | (1) |
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3.3 Problem 2: Master-Emulator Synchronization |
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93 | (1) |
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3.4 Problem 3: Slave-Emulator Synchronization |
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94 | (1) |
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3.5 Global Stability and Performance Analysis |
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95 | (3) |
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3.6 Tracking in Abrupt Changing Motion |
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98 | (1) |
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3.7 Tracking in Wall Contact Motion |
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98 | (1) |
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99 | (2) |
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99 | (2) |
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Graph Laplacian Design of a LTI Consensus System for the Largest Delay Margin: Case Studies |
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101 | (12) |
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101 | (1) |
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102 | (4) |
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102 | (1) |
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2.2 Stability, Responsible Eigenvalue (RE), Graph Synthesis |
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103 | (2) |
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105 | (1) |
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106 | (4) |
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3.1 Tailoring Stable 2(Ga) with Stable 2(Gb) |
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106 | (2) |
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3.2 Tailoring an Unstable System with a Stable System |
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108 | (2) |
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110 | (3) |
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111 | (2) |
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Second-Order Leaderless Consensus Protocols with Multiple Communication and Input Delays from Stability Perspective |
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113 | (14) |
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113 | (1) |
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114 | (4) |
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3 Stability Analysis Using CTCR Paradigm and SDS Domain |
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118 | (4) |
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4 Deployment on a Case Study |
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122 | (2) |
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124 | (3) |
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125 | (2) |
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Analysis of Gene Regulatory Networks under Positive Feedback |
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127 | (14) |
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127 | (2) |
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2 Notation, Preliminaries and Problem Formulation |
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129 | (2) |
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3 Analysis of the Cyclic Network under Positive Feedback |
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131 | (5) |
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3.1 General Conditions for Global Stability |
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131 | (1) |
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3.2 Analysis of Homogenous Gene Regulatory Networks |
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131 | (5) |
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136 | (3) |
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139 | (2) |
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139 | (2) |
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Analysis and Design of Pattern Formation in Networks of Nonlinear Systems with Delayed Couplings |
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141 | (14) |
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141 | (1) |
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2 Analysis of Oscillatory Patterns in Networks of Nonlinear Systems with Delayed Couplings |
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142 | (6) |
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2.1 Nonlinear Network Systems with Delayed Couplings |
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142 | (1) |
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2.2 Analysis of Periodic Solutions |
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143 | (3) |
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146 | (2) |
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3 Synthesis of Networks with Delays |
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148 | (5) |
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148 | (2) |
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150 | (3) |
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153 | (2) |
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153 | (1) |
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154 | (1) |
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Consensus in Networks of Discrete-Time Multi-agent Systems: Dynamical Topologies and Delays |
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155 | (16) |
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155 | (3) |
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158 | (3) |
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161 | (3) |
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4 Multi-agent Model with Nonlinear Coupling |
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164 | (1) |
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5 Numerical Examples: Dynamical Networks for Random Waypoint Model |
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165 | (2) |
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167 | (4) |
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167 | (4) |
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Part III Time-Delay and Sampled-Data Systems |
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Sampled-Data Stabilization under Round-Robin Scheduling |
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171 | (14) |
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171 | (2) |
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173 | (2) |
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175 | (7) |
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3.1 Stability Conditions for NCSs: Variable Sampling and Constant Input/Output Delay |
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175 | (3) |
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3.2 Stability Conditions for Sample-Data Systems: Constant vs Variable Sampling |
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178 | (4) |
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182 | (1) |
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183 | (2) |
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183 | (2) |
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Structure of Discrete Systems with Variable Nonlocal Behavior |
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185 | (14) |
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1 Introduction: Behavioral Approach |
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185 | (2) |
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187 | (1) |
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188 | (2) |
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188 | (1) |
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3.2 State Space and Trajectories |
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189 | (1) |
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4 Periodic Time Delay System |
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190 | (3) |
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5 Reflecto-difference Equation |
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193 | (4) |
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197 | (2) |
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197 | (2) |
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Decentralized Robustification of Interconnected Time-Delay Systems Based on Integral Input-to-State Stability |
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199 | (16) |
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199 | (2) |
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2 Idea and Issues to Be Solved |
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201 | (3) |
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3 Invariantly Differentiable Functionals |
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204 | (1) |
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4 Interconnected Time-Delay Systems with Discontinuous Right-Hand Side |
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205 | (2) |
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5 Decentralized iISS and ISS Feedback Redesign |
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207 | (3) |
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210 | (2) |
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212 | (3) |
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212 | (3) |
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Global Stability Analysis of Nonlinear Sampled-Data Systems Using Convex Methods |
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215 | (14) |
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1 Introduction to the Problem of Stability of Sampled-Data Systems |
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215 | (2) |
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217 | (3) |
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217 | (1) |
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218 | (1) |
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2.3 Sum-of-Squares Optimization |
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219 | (1) |
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220 | (3) |
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221 | (1) |
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3.2 The Asynchronous Case |
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222 | (1) |
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223 | (3) |
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4.1 Example 1: 1-D Nonlinear Dynamical System |
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224 | (1) |
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4.2 Example 2: Controlled Model of a Jet Engine |
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224 | (2) |
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4.3 Example 3: 1-D System, Unknown Sampling Period |
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226 | (1) |
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226 | (3) |
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226 | (3) |
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DDE Model-Based Control of Glycemia via Sub-cutaneous Insulin Administration |
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229 | (14) |
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229 | (2) |
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2 The Glucose-Insulin Model |
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231 | (2) |
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3 The Feedback Control Law |
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233 | (3) |
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236 | (2) |
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238 | (5) |
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239 | (4) |
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Part IV Computational and Software Tools |
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Eigenvalue Based Algorithms and Software for the Design of Fixed-Order Stabilizing Controllers for Interconnected Systems with Time-Delays |
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243 | (14) |
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243 | (2) |
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2 Preliminaries and Assumptions |
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245 | (1) |
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3 Spectral Properties and Stability |
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246 | (3) |
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3.1 Exponential Stability |
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246 | (1) |
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3.2 Continuity of the Spectral Abscissa and Strong Stability |
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246 | (3) |
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4 Robust Stabilization by Eigenvalue Optimization |
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249 | (1) |
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5 Illustration of the Software |
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250 | (5) |
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6 Duality with the H∞ Problem |
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255 | (2) |
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255 | (2) |
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Computer Aided Control System Design for Time Delay Systems Using MATLAB® |
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257 | (14) |
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257 | (1) |
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258 | (1) |
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259 | (2) |
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261 | (2) |
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5 Time / Frequency Domain Analyses and Visualizations |
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263 | (2) |
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265 | (2) |
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7 Possible Enhancements in CACSD |
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267 | (1) |
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268 | (3) |
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268 | (3) |
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Analysis and Control of Time Delay Systems Using the LambertWDDE Toolbox |
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271 | (14) |
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272 | (1) |
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1.1 Motivation and Background |
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272 | (1) |
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273 | (1) |
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2 Theory, Examples and Numerical Simulation |
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273 | (9) |
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273 | (1) |
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273 | (1) |
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2.3 Example 1 - Spectrum and Series Expansion in the Scalar Case |
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274 | (1) |
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2.4 Example 2 - Scalar Case Approximation Response |
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275 | (1) |
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276 | (1) |
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2.6 Example 3 - General Case Approximation |
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277 | (1) |
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2.7 Observability and Controllability |
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278 | (1) |
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2.8 Example 4 - Piecewise Observability and Controllability |
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279 | (1) |
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2.9 Placement of Dominant Poles |
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279 | (1) |
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2.10 Example 5 - Rightmost Eigenvalue Assignment |
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280 | (1) |
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2.11 Robust Control and Time Domain Specifications |
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281 | (1) |
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2.12 Decay Function for TDS |
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281 | (1) |
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2.13 Example 6 - Factor and Decay Rate |
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281 | (1) |
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282 | (3) |
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282 | (3) |
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H∞-Stability Analysis of (Fractional) Delay Systems of Retarded and Neutral Type with the Matlab Toolbox YALTA |
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285 | (14) |
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285 | (2) |
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2 Functionalities of YALTA |
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287 | (2) |
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2.1 Asymptotic Axes and Poles of High Modulus |
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288 | (1) |
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2.2 Stability Windows and Root Locus |
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288 | (1) |
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2.3 Approximation of Poles of Small Modulus |
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288 | (1) |
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2.4 H∞-stability Analysis |
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289 | (1) |
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289 | (2) |
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3.1 Continuation Algorithm |
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289 | (1) |
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290 | (1) |
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4 Examples of YALTA Application |
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291 | (5) |
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4.1 Example 1- Bifurcation Analysis of a Small Degree System |
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291 | (2) |
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4.2 Example 2- Stability of a Fractional System |
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293 | (1) |
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4.3 Example 3- Computational Aspects |
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294 | (1) |
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4.4 Example 4- Pade-2 Approximation |
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295 | (1) |
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296 | (3) |
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296 | (3) |
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QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples |
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299 | (16) |
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299 | (2) |
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300 | (1) |
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2 Algorithm for Spectrum Computation |
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301 | (2) |
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2.1 Mapping the Zero Level Curves |
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302 | (1) |
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303 | (3) |
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3.1 Spectral Features of Neutral Quasi-Polynomial |
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304 | (2) |
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4 Working with QPmR v.2 in Matlab |
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306 | (4) |
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307 | (3) |
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310 | (5) |
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311 | (4) |
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Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia |
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315 | (14) |
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316 | (1) |
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2 Mathematical Model of AML |
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317 | (2) |
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319 | (2) |
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4 Analysis of the i-th Compartmental Model |
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321 | (3) |
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321 | (2) |
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4.2 Model Linearization and Stability |
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323 | (1) |
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5 Numerical Example and Simulation Results |
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324 | (3) |
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327 | (2) |
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328 | (1) |
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The Influence of Time Delay on Crane Operator Performance |
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329 | (14) |
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329 | (3) |
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2 The Influence of Communication Delay on Bridge Crane Operators |
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332 | (4) |
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2.1 Experimental Protocol |
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332 | (2) |
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334 | (2) |
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3 Remote Operation of a Tower Crane |
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336 | (3) |
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339 | (4) |
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340 | (3) |
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Decomposing the Dynamics of Delayed Hodgkin-Huxley Neurons |
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343 | (16) |
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343 | (2) |
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2 Decomposition of Delayed Networks around Synchronous States |
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345 | (4) |
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2.1 Stability of Synchronous Equilibria and Periodic Orbits |
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348 | (1) |
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3 Synchrony of Delay Coupled Hodgkin-Huxley Neurons |
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349 | (7) |
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3.1 Stability of Synchronous Equilibria |
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350 | (3) |
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3.2 Stability of Synchronous Periodic Orbits |
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353 | (3) |
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4 Conclusion and Discussion |
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356 | (3) |
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356 | (3) |
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Practical Delay Modeling of Externally Recirculated Burned Gas Fraction for Spark-Ignited Engines |
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359 | (14) |
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359 | (3) |
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1.1 Why Exhaust Gas Recirculation? |
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360 | (1) |
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1.2 Necessity of a Virtual Composition Sensor |
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361 | (1) |
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1.3 Comparison with Diesel EGR |
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361 | (1) |
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362 | (4) |
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2.1 Dilution Dynamics and Transport Delay |
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362 | (2) |
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2.2 Transport Delay Description |
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364 | (1) |
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2.3 Estimation Strategy with Practical Identification Procedure |
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365 | (1) |
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366 | (3) |
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3.1 Experimental Setup and Indirect Validation Methodology from FAR Measurements |
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366 | (1) |
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3.2 First Validation: Variation of the Amount of Reintroduced EGR (Constant Delay) |
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367 | (2) |
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3.3 Second Validation: Torque Transients (Varying Delay) |
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369 | (1) |
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4 Conclusion and Perspectives |
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369 | (4) |
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371 | (2) |
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Design and Control of Force Feedback Haptic Systems with Time Delay |
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373 | (16) |
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373 | (2) |
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2 Optimal Design Method for Haptic Device |
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375 | (6) |
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375 | (1) |
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2.2 Mechanical Model of the Haptic Device |
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376 | (1) |
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2.3 Necessary and Sufficient Stability Condition |
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377 | (1) |
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2.4 Optimal Design Method for Haptic Device |
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378 | (3) |
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3 Proposed Force Feedback Architecture |
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381 | (4) |
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3.1 Design of the Virtual Wall and the State Observer |
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381 | (2) |
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3.2 Numerical Simulation Results |
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383 | (2) |
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385 | (4) |
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386 | (3) |
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Engineering a Genetic Oscillator Using Delayed Feedback |
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389 | (14) |
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Antonis Papachristodoulou |
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389 | (1) |
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390 | (1) |
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3 Oscillations Using Delayed Negative Feedback |
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391 | (4) |
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392 | (1) |
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393 | (2) |
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4 Coupled Delay Oscillators |
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395 | (4) |
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396 | (1) |
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4.2 Coupled Delay Oscillators |
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396 | (3) |
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399 | (4) |
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402 | (1) |
Index |
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403 | |