The book focuses on analysis and design for positive stochastic jump systems. By using multiple linear co-positive Lyapunov function method and linear programming technique, a basic theoretical framework is formed toward the issues of analysis and design for positive stochastic jump systems. This is achieved by providing an in-depth study on several major topics such as stability, time delay, finite-time control, observer design, filter design, and fault detection for positive stochastic jump systems. The comprehensive and systematic treatment of positive systems is one of the major features of the book, which is particularly suited for readers who are interested to learn non-negative theory. By reading this book, the reader can obtain the most advanced analysis and design techniques for positive stochastic jump systems.
Author(s): Wenhai Qi, Guangdeng Zong
Series: Studies in Systems, Decision and Control, 450
Publisher: Springer
Year: 2022
Language: English
Pages: 218
City: Singapore
Preface
Acknowledgements
Contents
Symbols
1 Introduction
1.1 Background
1.2 Markov Jump Systems
1.3 Semi-Markov Jump Systems
1.4 Positive Systems
1.5 Positive Stochastic Jump Systems
1.6 Organization of the Book
References
Part I Positive Delayed Markov Jump Systems
2 Exponential Stability and mathscrL1-Gain Analysis
2.1 Introduction
2.2 Problem Statements and Preliminaries
2.3 Exponential Stability Analysis
2.4 mathscrL1-gain Performance Analysis
2.5 Simulation
2.6 Conclusion
References
Part II Positive Semi-Markov Jump Systems
3 Stability and Stabilization
3.1 Introduction
3.2 Problem Statements and Preliminaries
3.3 Mean Stability Analysis
3.4 Controller Design
3.5 Simulation
3.6 Conclusion
References
4 mathscrL1-Gain and Control Synthesis
4.1 Introduction
4.2 Problem Statements and Preliminaries
4.3 Stochastic Stability Analysis
4.4 mathscrL1-Gain Performance Analysis
4.5 Controller Design
4.6 Simulation
4.7 Conclusion
References
5 Finite-Time mathscrL1 Control
5.1 Introduction
5.2 Problem Statements and Preliminaries
5.3 Finite-time Boundedness Analysis
5.4 mathcalL1 Finite-Time Boundedness Analysis
5.5 Controller Design
5.6 Simulation
5.7 Conclusion
References
Part III Positive Delayed Semi-Markov Jump Systems
6 mathscrL1 Control
6.1 Introduction
6.2 Problem Statements and Preliminaries
6.3 Stochastic Stability Analysis
6.4 mathscrL1-Gain Performance Analysis
6.5 Controller Design
6.6 Simulation
6.7 Conclusion
References
7 mathscrLinfty Control
7.1 Introduction
7.2 Problem Statements and Preliminaries
7.3 Stochastic Stability Analysis
7.4 mathscrLinfty-Gain Performance Analysis
7.5 Controller Design
7.6 Simulation
7.7 Conclusion
References
8 Robust Finite-Time Stabilization
8.1 Introduction
8.2 Problem Statements and Preliminaries
8.3 Finite-time Boundedness Analysis
8.4 mathcalL1 Finite-Time Boundedness Analysis
8.5 Controller Design
8.6 Simulation
8.7 Conclusion
References
9 Fault Detection
9.1 Introduction
9.2 Problem Statements and Preliminaries
9.3 Stochastic Stability Analysis
9.4 mathscrL1-Gain Performance Analysis
9.5 Fault Detection Filter Design
9.6 Simulation
9.7 Conclusion
References
Part IV Positive Fuzzy Semi-Markov Jump Systems
10 Stochastic Stability and mathcalL1-Gain Analysis
10.1 Introduction
10.2 Problem Statements and Preliminaries
10.3 Stochastic Stability Analysis
10.4 mathcalL1-Gain Performance Analysis
10.5 Simulation
10.6 Conclusion
References
11 Positive mathcalL1 Observer Design
11.1 Introduction
11.2 Problem Statements and Preliminaries
11.3 Stochastic Stability Analysis
11.4 mathcalL1-Gain Performance Analysis
11.5 mathcalL1 Fuzzy Observer Design
11.6 Simulation
11.7 Conclusion
References
12 Filter Design
12.1 Introduction
12.2 Problem Statements and Preliminaries
12.3 Stochastic Stability with mathcalL1-Gain Performance Analysis
12.4 mathcalL1 Filter Design
12.5 Simulation
12.6 Conclusion
References
Part V Summary
13 Conclusion and Future Research Direction
13.1 Conclusion
13.2 Future Research Direction
