1st Edition

Sliding Mode Control of Semi-Markovian Jump Systems

By Baoping Jiang, Hamid Reza Karimi Copyright 2022
    174 Pages 37 B/W Illustrations
    by CRC Press

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    This book presents analysis and design for a class of stochastic systems with semi-Markovian jump parameters. It explores systematic analysis of semi-Markovian jump systems via sliding mode control strategy which makes up the shortages in the analysis and design of stochastic systems. This text provides a novel estimation method to deal with the stochastic stability of semi-Markovian jump systems along with design of novel integral sliding surface. Finally, Takagi-Sugeno fuzzy model approach is brought to deal with system nonlinearities and fuzzy sliding mode control laws are provided to ensure the stabilization purpose.


    • Presents systematic work on sliding mode control (SMC) of semi-Markvoain jump systems.
    • Explores SMC methods, such as fuzzy SMC, adaptive SMC, with the presence of generally uncertain transition rates.
    • Provides novel method in dealing with stochastic systems with unknown switching information.
    • Proposes more general theories for semi-Markovian jump systems with generally uncertain transition rates.
    • Discusses practical examples to verify the effectiveness of SMC theory in semi-Markovian jump systems.

    This book aims at graduate and postgraduate students and for researchers in all engineering disciplines, including mechanical engineering, electrical engineering and applied mathematics, control engineering, signal processing, process control, control theory and robotics.

    1 Introduction

    1.1 Sliding Mode Control

    1.2 Semi-Markvoain Jump Systems

    1.3 Preview of This Book

    1.4 Some Useful Definitions and Lemmas

    1.5 Abbreviations and Notations

    2 Stochastic Stability of Semi-Markovian Jump Systems With Generally Uncertain

    Transition Rates

    2.1 Introduction

    2.2 System Description

    2.3 Stochastic Stability Analysis

    2.4 Numerical Example

    2.5 Conclusion

    3 Fuzzy Integral Sliding Mode Control of Semi-Markovian Jump Systems

    3.1 Introduction

    3.2 System Description

    3.3 Main Results

    3.4 Numerical Example

    3.5 Conclusion

    4 Fuzzy Sliding Mode Control For Finite-Time Synthesis of Semi-Markovian Jump Systems

    4.1 Introduction

    4.2 System Description

    4.3 Main Results

    4.4 Numerical Example

    4.5 Conclusion

    5 Adaptive Fuzzy Sliding Mode Control of Semi-Markovian Jump Systems

    5.1 Introduction

    5.2 System Description

    5.3 Main Results

    5.4 Numerical Example

    5.5 Conclusion

    6 Decentralized Adaptive Sliding Mode Control of Large-Scale Semi-Markovian Jump Systems

    6.1 Introduction

    6.2 System Description

    6.3 Main Results

    6.4 Numerical Example

    6.5 Conclusion

    7 Reduced-Order Adaptive Sliding Mode Control for Switching Semi-Markovian Jump Delayed Systems

    7.1 Introduction

    7.2 System Description

    7.3 Main Results

    7.4 Numerical Example

    7.5 Conclusion

    8 Outlook


    Dr. Baoping Jiang

    School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou 215009, China (e-mails: [email protected]).

    Baoping Jiang received the Ph.D. degree in control theory from the Ocean University of China, Qingdao, China, in 2019. From 2017 to 2019, he was a joint training Ph.D. Candidate with the Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy. In 2019, he joined the Suzhou University of Science and Technology, Suzhou, China, where he is an associate professor. His research interests include sliding mode control, stochastic systems, etc.

    Dr. Hamid Reza Karimi

    Department of Mechanical Engineering, Politecnico di Milano, 20156 Milan, Italy, Email: [email protected]

    Hamid Reza Karimi received the B.Sc. (First Hons.) degree in power systems from the Sharif University of Technology, Tehran, Iran, in 1998, and the M.Sc. and Ph.D. (First Hons.) degrees in control systems engineering from the University of Tehran, Tehran, in 2001 and 2005, respectively. He is currently Professor of Applied Mechanics with the Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy. From 2009-2016, he has been Full Professor of Mechatronics-Control Systems at University of Agder, Norway. His current research interests include control systems and mechatronics with applications to automotive control systems, robotics, vibration systems and wind energy.

    Prof. Karimi is currently the Editor-in-Chief of the Journal of Cyber-Physical Systems, Editor-in-Chief of the Journal of Machines, Editor-in-Chief of the International Journal of Aerospace System Science and Engineering, Editor-in-Chief of the Journal of Designs, Subject Editor of the IET Journal of Electronics Letters, Section Editor-in-Chief of the Journal of Electronics, Subject Editor of the Journal of Science Progress, Subject Editor for Journal of The Franklin Institute and a Technical Editor or Associate Editor for some international journals. He is a member of Agder Academy of Science and Letters and also a member of the IEEE Technical Committee on Systems with Uncertainty, the Committee on Industrial Cyber-Physical Systems, the IFAC Technical Committee on Mechatronic Systems, the Committee on Robust Control, and the Committee on Automotive Control. Prof. Karimi has been awarded as the 2016-2020 Web of Science Highly Cited Researcher in Engineering, the 2020 IEEE Transactions on Circuits and Systems Guillemin-Cauer Best Paper Award, August-Wilhelm-Scheer Visiting Professorship Award, JSPS (Japan Society for the Promotion of Science) Research Award, and Alexander-von-Humboldt-Stiftung research Award, for instance. He has also participated as keynote/plenary speaker, distinguished speaker or program chair for many international conferences in the areas of Control Systems, Robotics and Mechatronics.