Regular Papers

International Journal of Control, Automation and Systems 2020; 18(2): 431-438

Published online August 19, 2019

https://doi.org/10.1007/s12555-018-0107-9

© The International Journal of Control, Automation, and Systems

Asynchronous H∞ Control for Positive Discrete-time Markovian Jump Systems

Hui Shang, Wenhai Qi, and Guangdeng Zong*

Qufu Normal University

Abstract

This paper deals with the asynchronous H∞ control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H∞ performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest’s age-structured population dynamic model is illustrated to show the validity of the present design.

Keywords Asynchronous controller, Lyapunov-Krasovskii functional, positive Markovian jump systems, stochastic stability.

Article

Regular Papers

International Journal of Control, Automation and Systems 2020; 18(2): 431-438

Published online February 1, 2020 https://doi.org/10.1007/s12555-018-0107-9

Copyright © The International Journal of Control, Automation, and Systems.

Asynchronous H∞ Control for Positive Discrete-time Markovian Jump Systems

Hui Shang, Wenhai Qi, and Guangdeng Zong*

Qufu Normal University

Abstract

This paper deals with the asynchronous H∞ control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H∞ performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest’s age-structured population dynamic model is illustrated to show the validity of the present design.

Keywords: Asynchronous controller, Lyapunov-Krasovskii functional, positive Markovian jump systems, stochastic stability.

IJCAS
June 2024

Vol. 22, No. 6, pp. 1761~2054

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