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© 2016

Analysis and Design of Markov Jump Systems with Complex Transition Probabilities

Book

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 54)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
    Pages 1-20
  3. Partially Unknown TPs

    1. Front Matter
      Pages 21-21
    2. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 23-44
    3. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 45-56
    4. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 57-70
    5. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 71-85
  4. Piecewise Homogeneous TPs

    1. Front Matter
      Pages 87-87
    2. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 89-133
    3. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 135-171
    4. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 173-185
  5. Memory TPs

    1. Front Matter
      Pages 187-187
    2. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 189-205
    3. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 207-224
    4. Lixian Zhang, Ting Yang, Peng Shi, Yanzheng Zhu
      Pages 225-248
  6. Back Matter
    Pages 249-263

About this book

Introduction

The book addresses the control issues such as stability analysis, control synthesis and filter design of Markov jump systems with the above three types of TPs, and thus is mainly divided into three parts. Part I studies the Markov jump systems with partially unknown TPs. Different methodologies with different conservatism for the basic stability and stabilization problems are developed and compared. Then the problems of state estimation, the control of systems with time-varying delays, the case involved with both partially unknown TPs and uncertain TPs in a composite way are also tackled. Part II deals with the Markov jump systems with piecewise homogeneous TPs. Methodologies that can effectively handle control problems in the scenario are developed, including the one coping with the asynchronous switching phenomenon between the currently activated system mode and the controller/filter to be designed. Part III focuses on the Markov jump systems with memory TPs. The concept of σ-mean square stability is proposed such that the stability problem can be solved via a finite number of conditions. The systems involved with nonlinear dynamics (described via the Takagi-Sugeno fuzzy model) are also investigated. Numerical and practical examples are given to verify the effectiveness of the obtained theoretical results. Finally, some perspectives and future works are presented to conclude the book.

Keywords

Stochastic Switching Systems Complex Transition Probabilities Stability analysis Control synthesis Filter design Stochastic Jumping systems

Authors and affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  3. 3.& Electronic Engg, Level 3 (Room 3.26)The Univ of Adelaide, Sch of ElectricalAdelaideAustralia
  4. 4.Harbin Institute of TechnologySchool of AstronauticsHarbinChina

Bibliographic information

  • Book Title Analysis and Design of Markov Jump Systems with Complex Transition Probabilities
  • Authors Lixian Zhang
    Ting Yang
    Peng Shi
    Yanzheng Zhu
  • Series Title Studies in Systems, Decision and Control
  • Series Abbreviated Title Studies in Systems, Decision and Control
  • DOI https://doi.org/10.1007/978-3-319-28847-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-28846-8
  • Softcover ISBN 978-3-319-80439-2
  • eBook ISBN 978-3-319-28847-5
  • Series ISSN 2198-4182
  • Series E-ISSN 2198-4190
  • Edition Number 1
  • Number of Pages XVI, 263
  • Number of Illustrations 8 b/w illustrations, 39 illustrations in colour
  • Topics Control and Systems Theory
    Complexity
    Systems Theory, Control
    Applications of Nonlinear Dynamics and Chaos Theory
  • Buy this book on publisher's site
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Reviews

“This book collects some of the authors’ previous results on Markov jump systems (MJSs) subject to complex transition probabilities (TPs) as well as the original developments on the stability analysis of MJSs. … This book can be used in undergraduate and graduate study. It can be also suitable as a reference for engineers and researchers in the field of systems with jump Markov perturbations.” (Vasile Drăgan, Mathematical Reviews, January, 2017)