Analysis and Design of Singular Markovian Jump Systems

1. Front Matter

   Pages i-ix

   PDF

2. Introduction

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 1-15

3. Stability

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 17-52

4. Stabilization

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 53-109

5. \(H_\infty \) Control

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 111-159

6. Observer-Based Feedback Stabilization

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 161-178

7. Filtering

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 179-227

8. Adaptive Control

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 229-249

9. Applications of a Markov Process

   • Guoliang Wang, Qingling Zhang, Xinngang Yan

   Pages 251-281

10. Back Matter

    Pages 283-284

    PDF

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques.

Features of the book include:

·         study of the stability problem for SMJSs with general transition rate matrices (TRMs);

·         stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints;

·         mode-dependent and mode-independent H∞ control solutions with development of a type of disordered controller;

·         observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent;

·         consideration of robust H∞ filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering

·         development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corres

ponding closed-loop system states

·         applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays

Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course.

• Adaptive Control
• H-infinity Filtering
• LMIs
• Linear Matrix Inequalities
• Singular Markovian Jump Systems
• Singularly Perturbed Systems
• Time Delays

“In this monograph, up-to-date research development and literature review on the analysis and design of SMJSs and some valuable reference material are presented. It is a good book which can help the relevant researchers to explore SMJSs and carry on further research in the area.” (Shuping Ma, Mathematical Reviews, May, 2015)

“Many practical systems, such as mechanical, electrical, chemical, economic systems can be modeled by singular Markovian Jump systems (SMJSs) having dynamics changing abruptly. … the aim of the monograph is to present the state-of-the-art of SMJSs. … The book can be recommended to readers having good knowledge in analysis, probability theory and stochastic processes.” (Kurt Marti, zbMATH 1317.93002, 2015)

• Liaoning Shihua University, Fushun, China

  Guoliang Wang

• College of Sciences Institute of Systems Science, Northeastern University, Shenyang, China

  Qingling Zhang

• School of Engineering and Digital Arts, The University of Kent, Canterbury, United Kingdom

  Xinggang Yan

Guoliang Wang received the B.Sc., M.Sc. and Ph.D. degrees in Control Theory and Engineering from the Northeastern University, China, in 2004, 2007 and 2010, respectively. He is currently an Associate Professor in the School of Information and Control Engineering, Liaoning Shihua University, China. He has authored/co-authored over 40 publications. His research interests include Markovian jump systems, singular systems, stochastic control and filtering.

Qingling Zhang received the B.Sc. and M.Sc. degrees from the Mathematics Department and the Ph.D. degree from the Automatic Control Department of Northeastern University, China, in 1982, 1986, and 1995, respectively. Since 1997, he has been a Professor with Northeastern University. He is also a member of the University Teaching Advisory Committee of National Ministry of Education. He has published 16 books and more than 480 papers about control theory and applications. Dr. Zhang received 14 prizes from central and local governments for his research. He has also received the Golden Scholarship from Australia in 2000 and now holds a visiting professor position in the University of Kent awarded by the Royal Academy of Engineering in United Kingdom. His current research interests cover singular systems, networked control systems, stochastic control and robust control.

Xinggang Yan received the B.Sc. and M.Sc. degrees in Shaanxi Normal University and Qufu Normal University respectively, and received the Ph.D deg

ree in Control Engineering from the Automatic Control Department of Northeastern University, China, in 1997. Currently, he is a Lecturer in the School of Engineering and Digitalk Arts in the University of Kent. He is a member of IEEE. He has published more than 100 papers in the area of control theory and applications. His research interest includes nonlinear control, sliding mode control, decentralized control, time delay systems, observer design and fault detection and isolation.

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