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Reliable H∞ Control on Stochastic Delayed Markovian Jump System with Asynchronous Jumped Actuator Failure

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  • Control Theory and Applications
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Abstract

This paper studies the reliable H∞ control on stochastic delayed Markovian jump systems (SDMJSs) with asynchronous jumped actuator failure and uncertain transition rates (TRs). It is assumed that the actuator failure occurs randomly under a Markov process with its jumping mode different from the system’s one. A generalized functional Itô’s formula for the closed-loop SDMJSs with mixed asynchronous Markovian jump modes (AMJMs) is successfully established. By the generalized functional Itô’s formula and the mixed-mode-dependent Lyapunov functionals, a sufficient delay-dependent condition of the reliable H∞ controller design for the SDMJSs with mixed AMJMs is proposed via matrix manipulation and a relaxation method. Finally, an example on VTOL (vertical take-off and landing) helicopter system is given to demonstrate the feasibility and effectiveness of the presented controller design scheme.

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Authors and Affiliations

  1. Department of Arts and Sciences, Chengdu College of University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, China

    Wenpin Luo

  2. Key Laboratory of Electronic and Information Engineering of State Ethnic Affairs Commission, College of Electrical and Information Engineering, Southwest Minzu University, Chengdu, Sichuan, 610041, China

    Jun Yang

  3. Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Xinzhi Liu

Authors
  1. Wenpin Luo
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  2. Jun Yang
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  3. Xinzhi Liu
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Correspondence to Jun Yang.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Guangdeng Zong under the direction of Editor Hamid Reza Karimi. This work was supported by the Fundamental Research Funds for the Central Universities of the Southwest Minzu University (Grant no. 2018NQN03). The authors are truly grateful to the editor and the anonymous reviewers for their valuable suggestions.

Wenpin Luo received her B.S. degree from Sichuan Normal University, Chengdu, China, in 2004 and an M.S. degree from University of Electronic Science and Technology of China, Chengdu, China, in 2007, all in applied mathematics. She is currently an Associate Professor with the Department of Arts and Sciences, Chengdu College of University of Electronic Science and Technology of China, Chengdu, China. From 2018 to 2019, she was a visiting scholar at the University of Waterloo. Her current research interests include neural networks and stochastic control systems.

Jun Yang received his B.S. degree from Leshan Normal University, Leshan, China, in 2004 and a Ph.D. degree from University of Electronic Science and Technology of China, Chengdu, China, in 2009, all in applied mathematics. He is currently a Professor with the College of Electrical and Information Engineering, Southwest Minzu University, Chengdu, China. From 2018 to 2019, he was a visiting scholar at the University of Waterloo. His current research interests include fuzzy and stochastic control systems. He is an active reviewer for many international journals.

Xinzhi Liu received his B.Sc. degree in mathematics from Shandong Normal University, Jinan, China, in 1982, and his M.Sc. and Ph.D. degrees, in applied mathematics, from the University of Texas, Arlington, Texas, USA, in 1987 and 1988, respectively. He was a Post-Doctoral Fellow at the University of Alberta, Edmonton, Alberta, Canada, from 1988 to 1990. He joined the Department of Applied Mathematics, University of Waterloo, Waterloo, Canada, as an Assistant Professor in 1990, where he became an Associate Professor and a Full Professor, in 1994 and 1997, respectively. His research areas include systems analysis, stability theory, hybrid dynamical systems, impulsive control, complex dynamical networks, and communication security. He is the author or coauthor of over 300 research articles and two research monographs and twenty edited books.

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Luo, W., Yang, J. & Liu, X. Reliable H∞ Control on Stochastic Delayed Markovian Jump System with Asynchronous Jumped Actuator Failure. Int. J. Control Autom. Syst. 19, 618–631 (2021). https://doi.org/10.1007/s12555-020-0154-x

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