Contents
1 Introduction to Markovian Jump Systems 1
1.1 Background 1
1.1.1 Robust Stochastic Stability 2
1.1.2 Imprecise Jumping Parameters 3
1.1.3 Nonlinear Markovian Jump Systems 4
1.1.4 Practical Stability 5
1.1.5 Networked Control Systems 5
1.2 Model Description and Preliminaries 6
References 10
2 Robust Stochastic Stability 15
2.1 Introduction 15
2.2 Uncertain Markovian Jump Linear Systems with Time Delays 16
2.3 Robust Control 20
2.4 Robust H1 Disturbance Attenuation 31
2.5 Numerical Simulation 37
2.6 Summary 40
References 40
3 System with Imprecise Jumping Parameters 43
3.1 Introduction 43
3.2 Asynchronous and Extended Asynchronous Switching 45
3.2.1 Asynchronous Switching 47
3.2.2 Extended Asynchronous Switching 49
3.3 Stability Analysis Under the Two Switchings 51
3.3.1 Stability Analysis Under Asynchronous Switching 51
3.3.2 Stability Analysis Under Extended Asynchronous Switching 62
3.4 Numerical Simulation 74
3.4.1 Asynchronous Switching 74
3.4.2 Extended Asynchronous Switching 83
3.5 Summary 93
References 94
4 Nonlinear Markovian Jump Systems 97
4.1 Introduction 97
4.2 Description of Nonlinear Uncertain Jump System 98
4.3 Robust Adaptive Control for Nonlinear Uncertain Jump Systems 100
4.4 Numerical Simulation 108
4.5 Summary 111
References 112
5 Practical Stability 113
5.1 Introduction 113
5.2 Markovian Jump Nonlinear Systems with Time Delays 114
5.3 Comparison Principle 115
5.4 Practical Stability 116
5.5 Practical Controllability 119
5.6 Optimal Control 121
5.7 Summary 128
References 128
6 Networked Control System：A Markovian Jump System Approach 131
6.1 Introduction 131
6.2 Description of Networked Control Systems 132
6.3 Packet-Based Control for NCSs 134
6.4 Stochastic Modeling and Stabilization 137
6.4.1 The MJS Model of the Packet-Based Control Approach for NCSs 138
6.4.2 Stochastic Stability and Stabilization 140
6.5 Numerical Simulation 143
6.6 Summary 146
References 146
7 Applications Based on the Markov Jump Theory 149
7.1 Introduction 149
7.2 Robotic Manipulator System 152
7.2.1 Introduction to the System 152
7.2.2 Output Feedback Controller Based on High-Gain Observer 155
7.2.3 Markovian Model and Problem Statement 156
7.2.4 Stability Analysis 159
7.2.5 Numerical Simulation 165
7.3 Optimal Control Problem of MJLS 169
7.3.1 An Description of Optimal Control Problem 169
7.3.2 Two-Level Regulating Method 171
7.3.3 Two Special Cases 178
7.3.4 Numerical Simulation 184
7.4 Summary 186
References 187
Index 191