Sliding Mode Control of Uncertain Parameter-switching Hybrid Systems

Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems addresses the increasing demand for developing SMC technologies and comprehensively presents the new, state-of-the-art sliding mode control methodologies for uncertain parameter-switching hybrid systems. It establishes a unified framework for SMC of Markovian jump singular systems and proposes new SMC methodologies based on the analysis results. A series of problems are solved with new approaches for analysis and synthesis of switched hybrid systems, including stability analysis and stabilization, dynamic output feedback control, and SMC. A set of newly developed techniques (e.g. average dwell time, piecewise Lyapunov function, parameter-dependent Lyapunov function, cone complementary linearization) are exploited to handle the emerging mathematical/computational challenges.

Key features:

• Covers new concepts, new models and new methodologies with theoretical significance in system analysis and control synthesis
• Includes recent advances in Markovian jump systems, switched hybrid systems, singular systems, stochastic systems and time-delay systems
• Includes solved problems
• Introduces advanced techniques

Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems is a comprehensive reference for researchers and practitioners working in control engineering, system sciences and applied mathematics, and is also a useful source of information for senior undergraduate and graduates studying in these areas.

Ligang Wu received the PhD degree in Control Theory and Control Engineering in 2006 from Harbin Institute of Technology, China. He was a Research Associate at Imperial College London, UK, and The University of Hong Kong, Hong Kong; a Senior Research Associate at City University of Hong Kong, Hong Kong. Now, he is a Professor of Control Science and Engineering at Harbin Institute of Technology, Harbin, China. Prof. Wu’s current research interests include sliding mode control, switched hybrid systems, optimal control and filtering, aircraft control, and model reduction.
Prof. Wu has been in the editorial board of a number of international journals, including IEEE Transactions on Automatic Control, IEEE Access, Information Sciences, Signal Processing, IET Control Theory and Applications, Circuits Systems and Signal Processing, Multidimensional Systems and Signal Processing, and Neurocomputing. He is also an Associate Editor for the Conference Editorial Board, IEEE Control Systems Society.

Peng Shi received the PhD degree in Electrical Engineering from the University of Newcastle, Australia; the PhD degree in Mathematics from the University of South Australia; and the DSc degree from the University of Glamorgan, UK. He was a lecturer at the University of South Australia; a senior scientist in the Defence Science and Technology Organisation, Australia; and a professor at the University of Glamorgan, UK. Now, he is a professor at The University of Adelaide; and Victoria University, Australia. Prof. Shi's research interests include system and control theory, computational intelligence, and operational research.
Prof. Shi is a Fellow of the Institution of Engineering and Technology, and a Fellow of the Institute of Mathematics and its Applications. He has been in the editorial board of a number of international journals, including IEEE Transactions on Automatic Control; Automatica; IEEE Transactions on Fuzzy Systems; IEEE Transactions on Cybernetics; and IEEE Transactions on Circuits and Systems-I.

Xiaojie Su was born in Henan, China, in 1985. He received the B.E. degree in automation from Jiamusi University, Jiamusi, China, in 2008, the M.S. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2010, and the PhD degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2013. Currently, he is a Professor of College of Automation at Chongqing University, Chongqing, China. His research interests include sliding mode control, robust filtering, T-S fuzzy systems, and model reduction. As a Guest Editor, he has organized two special issues in Mathematical Problems in Engineering and Abstract and Applied Analysis, respectively.

Acknowledgements vii

List of Notations xi

List of Abbreviations xiii

1 Introduction 1

1.1 Sliding Mode Control 1

1.1.1 Fundamental Theory of SMC 1

1.1.2 Overview of SMC Methodologies 12

1.2 Uncertain Parameter-Switching Hybrid Systems 15

1.2.1 Analysis and Synthesis of Switched Hybrid Systems 15

1.2.2 Analysis and Synthesis of Markovian Jump Linear Systems 23

1.3 Contribution of the Book 24

1.4 Outline of the Book 26

Part One SMC of Markovian Jump Singular Systems 33

2 State Estimation and SMC of Markovian Jump Singular Systems 35

2.1 Introduction 35

2.2 System Description and Preliminaries 36

2.3 Stochastic Stability Analysis 37

2.4 Main Results 39

2.4.1 Observer and SMC Law Design 40

2.4.2 Sliding Mode Dynamics Analysis 41

2.5 Illustrative Example 45

2.6 Conclusion 47

3 Optimal SMC of Markovian Jump Singular Systems with Time-Delay 49

3.1 Introduction 49

3.2 System Description and Preliminaries 50

3.3 Bounded L2 Gain Performance Analysis 51

3.4 Main Results 54

3.4.1 Sliding Mode Dynamics Analysis 54

3.4.2 SMC Law Design 58

3.5 Illustrative Example 59

3.6 Conclusion 62

4 SMC of Markovian Jump Singular Systems with Stochastic Perturbation 63

4.1 Introduction 63

4.2 System Description and Preliminaries 64

4.3 Integral SMC 65

4.3.1 Sliding Mode Dynamics Analysis 65

4.3.2 SMC Law Design 67

4.4 Optimal H∞ Integral SMC 69

4.4.1 Performance Analysis and SMC Law Design 69

4.4.2 Computational Algorithm 74

4.5 Illustrative Example 75

4.6 Conclusion 80

Part Two SMC of Switched State-Delayed Hybrid Systems 81

5 Stability and Stabilization of Switched State-Delayed Hybrid Systems 83

5.1 Introduction 83

5.2 Continuous-Time Systems 84

5.2.1 System Description 84

5.2.2 Main Results 85

5.2.3 Illustrative Example 89

5.3 Discrete-Time Systems 90

5.3.1 System Description 90

5.3.2 Main Results 91

5.3.3 Illustrative Example 97

5.4 Conclusion 100

6 Optimal DOF Control of Switched State-Delayed Hybrid Systems 101

6.1 Introduction 101

6.2 Optimal L2-L∞ DOF Controller Design 102

6.2.1 System Description and Preliminaries 102

6.2.2 Main Results 103

6.2.3 Illustrative Example 113

6.3 Guaranteed Cost DOF Controller Design 117

6.3.1 System Description and Preliminaries 117

6.3.2 Main Results 118

6.3.3 Illustrative Example 127

6.4 Conclusion 131

7 SMC of Switched State-Delayed Hybrid Systems: Continuous-Time Case 133

7.1 Introduction 133

7.2 System Description and Preliminaries 134

7.3 Main Results 134

7.3.1 Sliding Mode Dynamics Analysis 134

7.3.2 SMC Law Design 138

7.4 Illustrative Example 142

7.5 Conclusion 148

8 SMC of Switched State-Delayed Hybrid Systems: Discrete-Time Case 149

8.1 Introduction 149

8.2 System Description and Preliminaries 150

8.3 Main Results 151

8.3.1 Sliding Mode Dynamics Analysis 151

8.3.2 SMC Law Design 157

8.4 Illustrative Example 158

8.5 Conclusion 161

Part Three SMC of Switched Stochastic Hybrid Systems 163

9 Control of Switched Stochastic Hybrid Systems: Continuous-Time Case 165

9.1 Introduction 165

9.2 System Description and Preliminaries 166

9.3 Stability Analysis and Stabilization 168

9.4 H∞ Control 172

9.4.1 H∞ Performance Analysis 172

9.4.2 State Feedback Control 174

9.4.3 H∞ DOF Controller Design 175

9.5 Illustrative Example 178

9.6 Conclusion 183

10 Control of Switched Stochastic Hybrid Systems: Discrete-Time Case 185

10.1 Introduction 185

10.2 System Description and Preliminaries 185

10.3 Stability Analysis and Stabilization 187

10.4 H∞ Control 192

10.5 Illustrative Example 196

10.6 Conclusion 200

11 State Estimation and SMC of Switched Stochastic Hybrid Systems 201

11.1 Introduction 201

11.2 System Description and Preliminaries 201

11.3 Main Results 203

11.3.1 Sliding Mode Dynamics Analysis 203

11.3.2 SMC Law Design 204

11.4 Observer-Based SMC Design 205

11.5 Illustrative Example 209

11.6 Conclusion 215

12 SMC with Dissipativity of Switched Stochastic Hybrid Systems 217

12.1 Introduction 217

12.2 Problem Formulation and Preliminaries 218

12.2.1 System Description 218

12.2.2 Dissipativity 219

12.3 Dissipativity Analysis 220

12.4 Sliding Mode Control 224

12.4.1 Sliding Mode Dynamics 224

12.4.2 Sliding Mode Dynamics Analysis 226

12.4.3 SMC Law Design 228

12.5 Illustrative Example 229

12.6 Conclusion 233

References 235

Index 263

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