Asynchronous H∞ control of Markov jump discrete-time systems with incomplete transition probability and unreliable links

Yaonan Shan; Kun She; Shouming Zhong; Jun Cheng; Yongbin Yu; Hongyao Deng

doi:10.1016/j.isatra.2021.04.044

Asynchronous H_∞ control of Markov jump discrete-time systems with incomplete transition probability and unreliable links

ISA Trans. 2022 Mar:122:218-231. doi: 10.1016/j.isatra.2021.04.044. Epub 2021 May 7.

Authors

Yaonan Shan¹, Kun She², Shouming Zhong³, Jun Cheng⁴, Yongbin Yu², Hongyao Deng⁵

Affiliations

¹ College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, 450002, PR China. Electronic address: ynanshan@126.com.
² School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, PR China.
³ School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, PR China.
⁴ College of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, PR China; School of Information Science and Engineering, Chengdu University, Chengdu, 610106, PR China.
⁵ College of Computer Engineering and Information, Yangtze Normal University, Chongqing, 408000, PR China.

PMID: 33993995
DOI: 10.1016/j.isatra.2021.04.044

Abstract

In this study, an asynchronous H_∞ state feedback controller is devised for Markov jump discrete-time systems (MJDTSs) with time-varying delay. "Asynchronous" means that the system switching mode θ_k, the controller mode ϑ_k and the quantizer mode λ_k are different from each other. The first one is homogeneous and the last two are non-homogeneous. In particular, as a promotion of existing work, we firstly attempt to propose the transition probabilities (TPs) of the three Markov chains (MCs) are not completely known. In addition, the discrete time-varying delay and its infinitely distributed ones are considered. Moreover, according to the Lyapunov stability theory and stochastic process, it is established for the sufficient criterion to ensure the stochastic stability of resulting closed-loop MJDTSs with an H_∞ attenuation performance index. The feasibility and effectiveness of the proposed method are validated by three examples.

Keywords: Asynchronous control; Incomplete transition probability (ITP); Markov jump discrete-time systems (MJDTSs); Mixed time-varying delay; Unreliable links.