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E-raamat: Linear Parameter-Varying and Time-Delay Systems: Analysis, Observation, Filtering & Control

  • Formaat: PDF+DRM
  • Sari: Advances in Delays and Dynamics 3
  • Ilmumisaeg: 03-Sep-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662440506
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Linear Parameter-Varying and Time-Delay Systems: Analysis, Observation, Filtering & ControlSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Advances in Delays and Dynamics 3
  • Ilmumisaeg: 03-Sep-2014
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662440506
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This book provides an introduction to the analysis and control of linear parameter-varying systems and time-delay systems and their interactions. The purpose is to give the readers some fundamental theoretical background on these topics and to give more insights on the possible applications of these theories. This self-contained monograph is written in an accessible way for readers ranging from undergraduate/PhD students to engineers and researchers willing to know more about the fields of time-delay systems, parameter-varying systems, robust analysis, robust control, gain-scheduling techniques in the LPV fashion and LMI based approaches. The only prerequisites are basic knowledge in linear algebra, ordinary differential equations and (linear) dynamical systems. Most of the results are proved unless the proof is too complex or not necessary for a good understanding of the results. In the latter cases, suitable references are systematically provided. The first part pertains on the

representation, analysis and control of LPV systems along with a reminder on robust analysis and control techniques. The second part is concerned with the representation and analysis of time-delay systems using various time-domain techniques. The third and last part is devoted to the representation, analysis, observation, filtering and control of LPV time-delay systems. The book also presents many basic and advanced results for the manipulation of LMIs, which is extensively used in this monograph.

Linear parameter-varying systems.- Time-Delay Systems.- Linear parameter-varying time-delay systems.

Arvustused

This book is a self-contained monograph that provides a large collection of results on linear parameter-varying (LPV) systems. The book is of interest to mathematicians and engineers working on LPV systems and/or time-delay control systems. (Iasson Karafyllis, Mathematical Reviews, November, 2015)

Part I Linear Parameter-Varying Systems
1 Introduction to LPV Systems
3(34)
1.1 System Definition
3(2)
1.2 Types of Parameters
5(4)
1.2.1 Approximating Nonlinear Systems: Quasi-LPV Systems
5(3)
1.2.2 Embedding Time-Varying Components: Intrinsic Parameters
8(1)
1.2.3 Artificial/Extrinsic Parameters
9(1)
1.3 Representation of LPV Systems
9(9)
1.3.1 Generic LPV Systems
10(1)
1.3.2 Polytopic LPV Systems
11(5)
1.3.3 LPV Systems in LFT-Form
16(2)
1.3.4 LPV Systems in Input/Output Form
18(1)
1.4 Examples
18(8)
1.4.1 Inverted Pendulum: Robust Control and Performance
19(1)
1.4.2 LPV Model for a Web Service System
20(2)
1.4.3 LPV Models for Aperiodic Sampled-Data Systems
22(1)
1.4.4 Automotive Suspension System
23(3)
1.4.5 A Wide Range of Applications
26(1)
1.5 Control, Observation and Filtering of LPV Systems
26(11)
1.5.1 Observation and Filtering of LPV Systems
27(1)
1.5.2 Control of LPV Systems
28(2)
References
30(7)
2 Stability of LPV Systems
37(56)
2.1
Chapter Outline
37(1)
2.2 General Notions of Stability for Dynamical Systems
38(5)
2.2.1 General Stability and Instability Results
39(2)
2.2.2 The LTI System Case
41(2)
2.3 Stability Notions for LPV and Uncertain Systems
43(8)
2.3.1 Quadratic Stability
44(2)
2.3.2 Robust Stability
46(3)
2.3.3 Stability with Brief Instabilities
49(1)
2.3.4 Other Types of Lyapunov Functions
49(2)
2.4 Stability of Generic LPV Systems
51(5)
2.4.1 Quadratic Stability
51(4)
2.4.2 Robust Stability
55(1)
2.5 Stability of Polytopic LPV Systems
56(6)
2.5.1 Quadratic Stability
56(1)
2.5.2 Robust Stability
57(5)
2.6 Stability of LPV Systems in LFT-Form
62(31)
2.6.1 L2-Norm and Hs-Norm
63(2)
2.6.2 Small-Gain Theorem
65(3)
2.6.3 Constant D-Scalings and the Scaled-Small Gain Theorem
68(2)
2.6.4 Frequency-Dependent D-Scalings
70(2)
2.6.5 Full-Block S-Procedure
72(4)
2.6.6 Topological and Quadratic Separation
76(8)
2.6.7 Integral Quadratic Constraints Analysis
84(4)
References
88(5)
3 Control of LPV Systems
93(30)
3.1 Gain-Scheduling: The LPV Way
93(1)
3.2 Types of Controllers
94(2)
3.2.1 Gain-Scheduled State-Feedback
95(1)
3.2.2 Gain-Scheduled Static-Output-Feedback
95(1)
3.2.3 Gain-Scheduled Dynamic-Output-Feedback
96(1)
3.3 Generic Parameter Dependent Systems
96(11)
3.3.1 Quadratic Stabilization by State-Feedback
97(4)
3.3.2 Quadratic Stabilization by Dynamic-Output Feedback
101(3)
3.3.3 Robust Stabilization by State-Feedback
104(1)
3.3.4 Robust Stabilization by Dynamic-Output Feedback
105(2)
3.4 Polytopic LPV Systems
107(2)
3.4.1 Quadratic Stabilization by State-Feedback
107(1)
3.4.2 Robust Stabilization by State-Feedback
108(1)
3.5 LPV Systems in LFT-Form
109(14)
3.5.1 Quadratic Stabilization by State-Feedback
111(4)
3.5.2 Quadratic Stabilization by Dynamic Output-Feedback
115(3)
References
118(5)
Part II Time-Delay Systems
4 Introduction to Time-Delay Systems
123(42)
4.1 Representation of Time-Delay Systems
123(2)
4.1.1 Functional Differential Equations
123(1)
4.1.2 Differential Equation with Coefficients in a Ring of Operators
124(1)
4.1.3 Abstract Representation Over an Infinite Dimensional Linear Space
124(1)
4.2 Bestiary of Time-Delay Systems and Delays
125(6)
4.2.1 Types of Time-Delay Systems
125(4)
4.2.2 Families of Delays
129(2)
4.3 Examples
131(17)
4.3.1 Delays in Biological Reaction Networks
131(3)
4.3.2 Aperiodic Sampled-Data Systems
134(2)
4.3.3 Delay-SIR Model
136(3)
4.3.4 Neutral Pearl-Verhulst Equation and Ecology
139(1)
4.3.5 Networks and Congestion Control Modeling
140(8)
4.4 Control, Observation and Filtering of Time-Delay Systems
148(17)
4.4.1 Observation and Filtering
149(2)
4.4.2 Control
151(4)
References
155(10)
5 Stability Analysis of Time-Delay Systems
165(80)
5.1
Chapter Outline
165(1)
5.2 General Notions of Stability for Time-Delay Systems
166(8)
5.2.1 Definitions
166(1)
5.2.2 General Stability and Instability Results
167(6)
5.2.3 LTI System Case
173(1)
5.3 Delay-Related Notions of Stability
174(5)
5.3.1 Delay-Independent Stability
175(1)
5.3.2 Delay-Dependent and Delay-Range Stability
176(2)
5.3.3 Time-Varying Delays and the Quenching Phenomenon
178(1)
5.4 Model Transformations, Comparison Systems and Additional Dynamics
179(4)
5.4.1 Newton-Leibniz Model Transformation
179(2)
5.4.2 Parametrized Newton-Leibniz Model Transformation
181(1)
5.4.3 Descriptor Model Transformation
182(1)
5.4.4 Other Model Transformations
183(1)
5.5 Lyapunov-Razumikhin Stability Results
183(4)
5.5.1 Delay-Independent Stability
184(1)
5.5.2 Delay-Dependent Stability
185(2)
5.6 Lyapunov-Krasovskii Stability Results
187(30)
5.6.1 Delay-Independent Stability
188(3)
5.6.2 Delay-Dependent Stability---Newton-Leibniz Model Transformation
191(2)
5.6.3 Delay-Dependent Stability---Parametrized Newton-Leibniz Model Transformation
193(1)
5.6.4 Delay-Dependent Stability---Park's Inequality
194(6)
5.6.5 Delay-Dependent Stability---Descriptor Model Transformation
200(3)
5.6.6 Delay-Dependent Stability---Method of Free-Weighting Matrices
203(2)
5.6.7 Delay-Dependent Stability---Jensen's Inequality
205(7)
5.6.8 Fragmented Lyapunov-Krasovskii Functional
212(1)
5.6.9 Delay-Dependent Stability---Wirtinger's Inequality
213(4)
5.7 L2 Scaled Small-Gain Theorem Based Results
217(6)
5.7.1 Delay Operators
217(4)
5.7.2 Delay-Independent Stability
221(1)
5.7.3 Delay-Dependent Stability
222(1)
5.7.4 Final Remarks
223(1)
5.8 QLx Scaled Small-Gain Theorem Based Results
223(8)
5.8.1 *-Bounded Real Lemma and QLx Scaled Small-Gain Theorem
224(3)
5.8.2 Norms of Delay-Operators
227(1)
5.8.3 Delay-Independent Stability
228(1)
5.8.4 Delay-Dependent Stability
229(2)
5.9 Integral Quadratic Constraints
231(3)
5.9.1 Delay-Independent Stability
231(1)
5.9.2 Delay-Dependent Stability
232(2)
5.10 Quadratic Separation
234(11)
5.10.1 Preliminary Results
234(1)
5.10.2 Delay-Independent Stability
235(1)
5.10.3 Delay-Dependent Stability
236(1)
References
237(8)
Part III Linear Parameter-Varying Time-Delay Systems
6 Introduction to LPV Time-Delay Systems
245(20)
6.1 Representation of LPV Time-Delay Systems
245(2)
6.1.1 Coupling Between Delays and Parameters
246(1)
6.2 Examples
247(8)
6.2.1 Milling Process
247(1)
6.2.2 LPV Control of a System with Input Delay
248(2)
6.2.3 Approximation of State-Dependent Delay Systems
250(1)
6.2.4 LPV Model of a Marine Cooling System
251(3)
6.2.5 Other Applications
254(1)
6.3 Stability Results for LPV Time-Delay Systems
255(10)
6.3.1 Case of Parameter-Dependent Delay
260(1)
6.3.2 Case of Delayed Parameters
261(1)
References
262(3)
7 Observation and Filtering of LPV Time-Delay Systems
265(28)
7.1 Observation of LPV Time-Delay Systems
265(16)
7.1.1 Observer with Exact Memory
266(5)
7.1.2 Examples
271(5)
7.1.3 Memoryless Observer
276(3)
7.1.4 Examples
279(2)
7.2 Simple Observers for LPV Time-Delay Systems
281(3)
7.2.1 Observer with Exact-Memory
281(1)
7.2.2 Memoryless Observer
282(2)
7.3 Filtering of LPV Time-Delay Systems
284(9)
7.3.1 Filter with Exact Memory
285(2)
7.3.2 Memoryless Filter
287(1)
7.3.3 Examples
288(3)
References
291(2)
8 Control of LPV Time-Delay Systems
293(42)
8.1 State-Feedback Controllers
293(22)
8.1.1 Delay-Independent Stabilization---Generic Case
294(2)
8.1.2 Delay-Dependent Stabilization---Generic Case
296(11)
8.1.3 Delay-Independent Stabilization---LFT Case
307(4)
8.1.4 Delay-Dependent Stabilization---LFT Case
311(4)
8.1.5 Further Remarks on LFT-Based Approaches
315(1)
8.2 Observer-Based Output Feedback Controllers
315(12)
8.2.1 Memoryless Observer-Based Output Feedback
316(7)
8.2.2 Observer-Based Output Feedback with Exact Memory
323(4)
8.3 Dynamic Output-Feedback Controllers
327(8)
8.3.1 Dynamic Output Feedback with Exact Memory
327(5)
8.3.2 Memoryless Dynamic Output Feedback
332(1)
References
333(2)
Appendix A Technical Results in Linear Algebra 335(6)
Appendix B Linear Matrix Inequalities 341(18)
Appendix C Technical Results in Robust Analysis, Control and LMIs 359(32)
Index 391
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