Sun Stability Theory of Switched Dynamical Systems

1. Auflage 2011
ISBN: 978-0-85729-256-8
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 256 Seiten

There are plenty of challenging and interesting problems open for investigation in the field of switched systems. Stability issues help to generate many complex nonlinear dynamic behaviors within switched systems. The authors present a thorough investigation of stability effects on three broad classes of switching mechanism: arbitrary switching where stability represents robustness to unpredictable and undesirable perturbation, constrained switching, including random (within a known stochastic distribution), dwell-time (with a known minimum duration for each subsystem) and autonomously-generated (with a pre-assigned mechanism) switching; and designed switching in which a measurable and freely-assigned switching mechanism contributes to stability by acting as a control input.

For each of these classes this book propounds: detailed stability analysis and/or design, related robustness and performance issues, connections to other control problems and many motivating and illustrative examples.

Autoren/Hrsg.

Sun, Zhendong

Inhaltsverzeichnis

1;Preface;7
1.1;Acknowledgments;10
1.2;Financial Support;11
2;Contents;12
3;List of Symbols;15
4;Introduction;18
4.1;1.1 Switched Dynamical Systems;18
4.2;1.2 Stability and Stabilizability of Switched Systems;21
4.2.1;1.2.1 Guaranteed Stability Under Arbitrary Switching;22
4.2.2;1.2.2 Dwell-Time Stability;23
4.2.3;1.2.3 Autonomous Stability Under State-Driven Switching;25
4.2.4;1.2.4 Stochastic Stabilities Under Random Switching;26
4.2.5;1.2.5 Stabilizing Switching Design;28
4.3;1.3 Organization of the Book;29
4.4;1.4 Notes and References;31
5;Arbitrary Switching;33
5.1;2.1 Preliminaries;33
5.2;2.2 Switched Nonlinear Systems;35
5.2.1;2.2.1 Common Lyapunov Functions;36
5.2.2;2.2.2 Converse Lyapunov Theorem;39
5.3;2.3 Switched Linear Systems;41
5.3.1;2.3.1 Relaxed System Frameworks;42
5.3.2;2.3.2 Universal Lyapunov Functions;46
5.3.3;2.3.3 Algebraic Criteria;51
5.3.4;2.3.4 Extended Coordinate Transformation and Set Invariance;57
5.3.5;2.3.5 Triangularizable Systems;64
5.4;2.4 Computational Issues;68
5.4.1;2.4.1 Approximating the Spectral Radius;68
5.4.2;2.4.2 An Invariant Set Approach;78
5.5;2.5 Notes and References;81
6;Constrained Switching;86
6.1;3.1 Introduction;86
6.2;3.2 Stochastic Stability;86
6.2.1;3.2.1 Introduction;86
6.2.2;3.2.2 Definitions and Preliminaries;87
6.2.3;3.2.3 Stability Criteria;88
6.3;3.3 Piecewise Linear Systems ;101
6.3.1;3.3.1 Introduction;101
6.3.2;3.3.2 Piecewise Quadratic Lyapunov Function Approach;103
6.3.3;3.3.3 Surface Lyapunov Approach;107
6.3.4;3.3.4 Transition Analysis: A Graphic Approach;115
6.3.5;3.3.5 Conewise Linear Systems;120
6.4;3.4 Dwell-Time Switching;127
6.4.1;3.4.1 Preliminaries;128
6.4.2;3.4.2 Homogeneous Polynomial Lyapunov Approach;134
6.4.3;3.4.3 Combined Switching;137
6.5;3.5 Notes and References;139
7;Designed Switching;142
7.1;4.1 Preliminaries;142
7.2;4.2 Stabilization via Time-Driven Switching;143
7.3;4.3 Stabilization via State-Feedback Switching: The Lyapunov Approach;148
7.3.1;4.3.1 Converse Lyapunov Theorems;149
7.3.2;4.3.2 Nonconvexity of Lyapunov Functions;155
7.3.3;4.3.3 Min Quadratic Lyapunov Functions: An Optimization Approach;159
7.3.4;4.3.4 Well-Definedness of State-Feedback Stabilizing Law;170
7.4;4.4 Stabilization via Mixed-Driven Switching: Aggregation and Calculation;171
7.4.1;4.4.1 Pathwise State-Feedback Switching;172
7.4.2;4.4.2 Computational Algorithms;179
7.5;4.5 Stabilization via Mixed-Driven Switching: Robustness Analysis;185
7.5.1;4.5.1 Distance Between Switching Signals;186
7.5.2;4.5.2 Robustness Analysis;192
7.5.3;4.5.3 Examples and Simulations;198
7.6;4.6 Notes and References;208
8;Connections and Implications;211
8.1;5.1 Absolute Stability for Planar Lur'e Systems;211
8.1.1;5.1.1 Guaranteed Stability in the Plane;212
8.1.2;5.1.2 Application to Absolute Stability of Planar Lur'e Systems;217
8.2;5.2 Adaptive Control via Supervisory Switching;219
8.2.1;5.2.1 Preliminaries;220
8.2.2;5.2.2 Estimator-based Supervisory Switching;222
8.2.3;5.2.3 An Example;226
8.3;5.3 Stability Analysis of Fuzzy Systems via Piecewise Switching;229
8.3.1;5.3.1 Piecewise Switched Linear Systems;230
8.3.2;5.3.2 Stability Analysis of T-S Fuzzy Systems;232
8.4;5.4 Consensus of Multiagent Systems with Proximity Graphs ;235
8.4.1;5.4.1 Introduction;235
8.4.2;5.4.2 A Consensus Criterion;237
8.4.3;5.4.3 A Verifiable Criterion;239
8.5;5.5 Stabilizing Design of Controllable Switched Linear Systems ;245
8.5.1;5.5.1 Problem Formulation;245
8.5.2;5.5.2 Multilinear Feedback Design;245
8.6;5.6 Notes and References;250
9;References;253
10;Index;264