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H∞ mean square finite-time control for Markov jump linear system with multiple equilibria

Lookup NU author(s): Dr Wanqing ZhaoORCiD

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Abstract

© IMechE 2024.In this article, the mean square finite-time (Formula presented.) control problems of two types of Markov jump linear system with multiple equilibria are investigated. To be specific, Markov jump linear system with multiple equilibria in discrete-time domain and continuous-time domain are considered, respectively, in which the equilibria of subsystems are different. First, an average equilibrium is introduced to equivalently reformulate the initial system expressions. Following this method, some sufficient conditions guaranteeing that Markov jump linear system with multiple equilibria subjected to norm bounded disturbance is mean square finite-time boundedness are proposed, and the results are extended to (Formula presented.) mean square finite-time boundedness. Then, mean square finite-time (Formula presented.) controllers are designed separately to stabilize the two types of Markov jump linear system with multiple equilibria and also achieve the prescribed (Formula presented.) performance index. The proposed methods in this article are a natural generalization of typical results in Markov jump linear system sharing common equilibrium. Finally, two numerical examples are exploited to demonstrate the effectiveness of the methods proposed in this article.

Publication metadata

Author(s): Gao W, Song Y, Liu Y, Zhao W

Publication type: Article

Publication status: Published

Journal: Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

Year: 2024

Volume: 238

Issue: 8

Pages: 1505-1517

Print publication date: 01/09/2024

Online publication date: 21/02/2024

Acceptance date: 02/01/2024

ISSN (print): 0959-6518

ISSN (electronic): 2041-3041

Publisher: SAGE Publications Ltd

URL: https://doi.org/10.1177/09596518241227497

DOI: 10.1177/09596518241227497

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