Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

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.

• Preface v Acknowledgements viiList of Notations xiList of Abbreviations xiii1 Introduction 11.1 Sliding Mode Control 11.1.1 Fundamental Theory of SMC 11.1.2 Overview of SMC Methodologies 121.2 Uncertain Parameter-Switching Hybrid Systems 151.2.1 Analysis and Synthesis of Switched Hybrid Systems 151.2.2 Analysis and Synthesis of Markovian Jump Linear Systems 231.3 Contribution of the Book 241.4 Outline of the Book 26Part One SMC of Markovian Jump Singular Systems 332 State Estimation and SMC of Markovian Jump Singular Systems 352.1 Introduction 352.2 System Description and Preliminaries 362.3 Stochastic Stability Analysis 372.4 Main Results 392.4.1 Observer and SMC Law Design 402.4.2 Sliding Mode Dynamics Analysis 412.5 Illustrative Example 452.6 Conclusion 473 Optimal SMC of Markovian Jump Singular Systems with Time-Delay 493.1 Introduction 493.2 System Description and Preliminaries 503.3 Bounded L2 Gain Performance Analysis 513.4 Main Results 543.4.1 Sliding Mode Dynamics Analysis 543.4.2 SMC Law Design 583.5 Illustrative Example 593.6 Conclusion 624 SMC of Markovian Jump Singular Systems with Stochastic Perturbation 634.1 Introduction 634.2 System Description and Preliminaries 644.3 Integral SMC 654.3.1 Sliding Mode Dynamics Analysis 654.3.2 SMC Law Design 674.4 Optimal H∞ Integral SMC 694.4.1 Performance Analysis and SMC Law Design 694.4.2 Computational Algorithm 744.5 Illustrative Example 754.6 Conclusion 80Part Two SMC of Switched State-Delayed Hybrid Systems 815 Stability and Stabilization of Switched State-Delayed Hybrid Systems 835.1 Introduction 835.2 Continuous-Time Systems 845.2.1 System Description 845.2.2 Main Results 855.2.3 Illustrative Example 895.3 Discrete-Time Systems 905.3.1 System Description 905.3.2 Main Results 915.3.3 Illustrative Example 975.4 Conclusion 1006 Optimal DOF Control of Switched State-Delayed Hybrid Systems 1016.1 Introduction 1016.2 Optimal L2-L∞ DOF Controller Design 1026.2.1 System Description and Preliminaries 1026.2.2 Main Results 1036.2.3 Illustrative Example 1136.3 Guaranteed Cost DOF Controller Design 1176.3.1 System Description and Preliminaries 1176.3.2 Main Results 1186.3.3 Illustrative Example 1276.4 Conclusion 1317 SMC of Switched State-Delayed Hybrid Systems: Continuous-Time Case 1337.1 Introduction 1337.2 System Description and Preliminaries 1347.3 Main Results 1347.3.1 Sliding Mode Dynamics Analysis 1347.3.2 SMC Law Design 1387.4 Illustrative Example 1427.5 Conclusion 1488 SMC of Switched State-Delayed Hybrid Systems: Discrete-Time Case 1498.1 Introduction 1498.2 System Description and Preliminaries 1508.3 Main Results 1518.3.1 Sliding Mode Dynamics Analysis 1518.3.2 SMC Law Design 1578.4 Illustrative Example 1588.5 Conclusion 161Part Three SMC of Switched Stochastic Hybrid Systems 1639 Control of Switched Stochastic Hybrid Systems: Continuous-Time Case 1659.1 Introduction 1659.2 System Description and Preliminaries 1669.3 Stability Analysis and Stabilization 1689.4 H∞ Control 1729.4.1 H∞ Performance Analysis 1729.4.2 State Feedback Control 1749.4.3 H∞ DOF Controller Design 1759.5 Illustrative Example 1789.6 Conclusion 18310 Control of Switched Stochastic Hybrid Systems: Discrete-Time Case 18510.1 Introduction 18510.2 System Description and Preliminaries 18510.3 Stability Analysis and Stabilization 18710.4 H∞ Control 19210.5 Illustrative Example 19610.6 Conclusion 20011 State Estimation and SMC of Switched Stochastic Hybrid Systems 20111.1 Introduction 20111.2 System Description and Preliminaries 20111.3 Main Results 20311.3.1 Sliding Mode Dynamics Analysis 20311.3.2 SMC Law Design 20411.4 Observer-Based SMC Design 20511.5 Illustrative Example 20911.6 Conclusion 21512 SMC with Dissipativity of Switched Stochastic Hybrid Systems 21712.1 Introduction 21712.2 Problem Formulation and Preliminaries 21812.2.1 System Description 21812.2.2 Dissipativity 21912.3 Dissipativity Analysis 22012.4 Sliding Mode Control 22412.4.1 Sliding Mode Dynamics 22412.4.2 Sliding Mode Dynamics Analysis 22612.4.3 SMC Law Design 22812.5 Illustrative Example 22912.6 Conclusion 233References 235 Index 263