Stability Theory of Switched Dynamical Systems (eBook)

Zhendong Sun obtained his Ph.D. degree at the Beijing University of Aeronautics and Astronautics in 1996. He was a Postdoctoral Research Fellow in the Department of Automation, Tsinghua University. From 1998 to 2002, he was with the Faculty of Science, Beijing University of Aeronautics and Astronautics, as an Associate Professor. During this period, he visited the Department of Electrical and Computer Engineering, National University of Singapore, and the School of Electrical Engineering and Telecommunications, University of New South Wales, both as a Research Fellow. From 2002 to 2005, he worked at the Hamilton Institute, National University of Ireland, Maynooth, as a Senior Research Fellow. He joined the Center of Control and Optimization, South China University of Technology in September 2005, and is currently a Full Professor and a Distinguished Young Lecturer.Dr. Sun's current research interests are in the fields of nonlinear control systems, switched and hybrid systems, and sampled-data systems. He is author of the book Switched Linear Systems (Springer, 2005). He was the recipient of the Guan Zhao-Zhi Award at the Chinese Control Conference (HongKong, China) in 2000. He was nominated as an Outstanding Reviewer for Automatica in 2004. Since 2004, he has been an Associate Editor on the Conference Editorial Board of the IEEE Control Systems Society. He is currently supported by the New Century Talents’ Program of the Ministry of Education of China. He is a senior member of the IEEE.Shuzhi Sam Ge is the Director of Social Robotics Lab of Interactive Digital Media Institute, and a Professor of the Department of Electrical and Computer Engineering at the National University of Singapore. Dr Ge was the recipient of the 1999 National Technology Award, 2001 University Young Research Award, 2002 Temasek Young Investigator Award, Singapore, and the 2004 Outstanding Overseas Young Researcher Award from the Chinese National Science Foundation. He was elected to the Fellowship of the IEEE in 2006.He has (co)-authored three books: Adaptive Neural Network Control of Robotic Manipulators (World Scientific, 1998), Stable Adaptive Neural Network Control (Kluwer, 2001) and Switched Linear Systems (Springer, 2005); and edited one: Autonomous Mobile Robots (Taylor and Francis (CRC Press), 2006), and over 300 international journal and conference papers. He is/has been Associate Editor for a number of flagship journals including IEEE Transactions on Automatic Control, IEEE Transactions on Control Systems Technology, IEEE Transactions on Neural Networks, and Automatica. He is also one of the Series Editors (with Professor Frank Lewis of the University of Texas) of the Taylor & Francis (CRC Press) Automation and Control Engineering Series, and as an elected member of the Board of Governors of the IEEE Control Systems Society. His current research interests include social robotics, multimedia fusion, adaptive control, and intelligent systems.

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