New stability criteria for semi-Markov jump linear systems with time-varying delays

Wentao Le; Yucai Ding; Wenqing Wu; Hui Liu; Wentao Le; Yucai Ding; Wenqing Wu; Hui Liu

doi:10.3934/math.2021263

AIMS Mathematics

2021, Volume 6, Issue 5: 4447-4462. doi: 10.3934/math.2021263

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Research article

New stability criteria for semi-Markov jump linear systems with time-varying delays

School of science, Southwest University of Science and Technology, Mianyang, 621010, China

Received: 05 December 2020 Accepted: 08 February 2021 Published: 22 February 2021
MSC : 93B52, 93C42

In this paper, the delay-dependent stochastic stability problem of semi-Markov jump linear systems (S-MJLS) with time-varying delays is investigated. By constructing a Lyapunov-Krasovskii functional (LKF) with two delay-product-type terms, a new sufficient condition on stochastic stability of S-MJLSs is derived in terms of linear matrix inequalities (LMIs). Furthermore, the combination use of a slack condition on Lyapunov matrix and the improved Wirtinger's integral inequality reduces the conservatism of the result. Numerical examples are provided to verify the effectiveness and superiority of the presented results.
- semi-Markov jump linear systems,
- time-varying delays,
- delay-dependent stability,
- Wirtinger's integral inequality
Citation: Wentao Le, Yucai Ding, Wenqing Wu, Hui Liu. New stability criteria for semi-Markov jump linear systems with time-varying delays[J]. AIMS Mathematics, 2021, 6(5): 4447-4462. doi: 10.3934/math.2021263

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Abstract

In this paper, the delay-dependent stochastic stability problem of semi-Markov jump linear systems (S-MJLS) with time-varying delays is investigated. By constructing a Lyapunov-Krasovskii functional (LKF) with two delay-product-type terms, a new sufficient condition on stochastic stability of S-MJLSs is derived in terms of linear matrix inequalities (LMIs). Furthermore, the combination use of a slack condition on Lyapunov matrix and the improved Wirtinger's integral inequality reduces the conservatism of the result. Numerical examples are provided to verify the effectiveness and superiority of the presented results.

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