1. Introduction |
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1 | (6) |
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3 | (4) |
2. Linear Time-Varying Systems |
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7 | (24) |
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2.1 Existence and Uniqueness |
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7 | (1) |
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2.2 The State Transition Matrix |
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8 | (3) |
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2.3 Lyapunov Stability of Linear Time-Varying Systems |
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11 | (4) |
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2.4 Sufficient Conditions for Exponential Stability |
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15 | (3) |
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2.5 Input-Output Gain of a Linear Time-Varying System |
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18 | (5) |
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2.6 Discrete-Time Systems |
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23 | (4) |
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2.6.1 Lyapunov Stability of Discrete-Time Systems |
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25 | (2) |
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27 | (1) |
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28 | (3) |
3. Quadratic Stability |
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31 | (62) |
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3.1 Necessary and Sufficient Conditions for Quadratic Stability |
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31 | (14) |
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43 | (2) |
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3.2 The General Nonlinear Parameter Dependence Case |
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45 | (13) |
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3.2.1 Polynomial Dependence on Parameters |
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45 | (1) |
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3.2.2 The Polytopic Covering Technique |
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46 | (12) |
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3.3 Other Approaches for Quadratic Stability Analysis |
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58 | (5) |
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58 | (1) |
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3.3.2 A Statistical Approach |
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59 | (3) |
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3.3.3 A Comparison Between the Various Methods for Quadratic Stability Analysis |
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62 | (1) |
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3.4 Quadratic Stability and Performances |
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63 | (7) |
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3.4.1 Quadratic Stability and Pole Placement (Quadratic D-Stability) |
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63 | (3) |
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3.4.2 Quadratic L2 Performance |
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66 | (2) |
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3.4.3 Quadratic Guaranteed Cost |
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68 | (2) |
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3.5 Norm Bounded Uncertainties |
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70 | (14) |
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3.5.1 The Multi-Block Case |
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75 | (3) |
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3.5.2 Quadratic Stability and Performances |
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78 | (6) |
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3.6 Connections between Quadratic Stability and 7-G, Control |
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84 | (5) |
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89 | (2) |
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91 | (2) |
4. Systems Depending on Bounded Rate Uncertainties |
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93 | (20) |
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4.1 Quadratic Stability via Parameter Dependent Lyapunov Functions |
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93 | (2) |
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4.2 Multi-Affine Quadratic Stability |
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95 | (4) |
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4.3 Polynomial Quadratic Stability |
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99 | (3) |
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4.4 A More General Class of Parameter Dependent Lyapunov Functions |
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102 | (6) |
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108 | (2) |
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110 | (3) |
5. Controller Design |
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113 | (38) |
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5.1 Quadratic Stabilization |
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113 | (13) |
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5.1.1 Quadratic Stabilization via State Feedback |
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113 | (2) |
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5.1.2 Quadratic Stabilization via Output Feedback |
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115 | (11) |
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5.2 Quadratic Stabilization with Performances |
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126 | (8) |
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5.2.1 Quadratic D-Stabilization |
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126 | (4) |
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5.2.2 Quadratic r2 Performance Control |
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130 | (3) |
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5.2.3 Guaranteed Cost Control |
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133 | (1) |
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5.3 Robust Stabilization in the Presence of Bounded Rate Parameters |
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134 | (2) |
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5.4 Systems Depending on Norm Bounded Uncertainties |
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136 | (11) |
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5.4.1 Quadratic Stabilization |
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136 | (4) |
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5.4.2 Quadratic Stabilization and Performances |
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140 | (7) |
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147 | (2) |
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149 | (2) |
6. Discrete-Time Systems |
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151 | (22) |
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151 | (4) |
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6.1.1 Parametric Uncertainties |
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151 | (2) |
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6.1.2 Norm Bounded Uncertainties |
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153 | (1) |
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6.1.3 Connections Between Quadratic Stability and Hinfinity Control |
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154 | (1) |
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6.2 Systems Subject to Bounded Rate Parameters |
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155 | (4) |
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6.2.1 Connections with the Quadratic Stability Approach |
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159 | (1) |
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6.3 A Real World Example: Control of a Plasma Wind Tunnel |
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159 | (7) |
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161 | (1) |
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6.3.2 Implementation Aspects and Numerical Results |
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162 | (4) |
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6.4 Quadratic Stabilization |
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166 | (3) |
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6.4.1 Parametric Uncertainties |
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166 | (2) |
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6.4.2 Norm Bounded Uncertainties |
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168 | (1) |
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169 | (2) |
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171 | (2) |
A. Appendix |
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173 | (12) |
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173 | (2) |
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A.2 Kronecker Product and Sum |
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175 | (1) |
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A.3 The Lyapunov Equation |
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176 | (3) |
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A.3.1 Some Useful Inequalities |
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177 | (1) |
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A.3.2 Discrete-Time Lyapunov Equation |
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177 | (2) |
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179 | (6) |
References |
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185 | (10) |
Index |
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195 | |