The moment exponential stability of infinite-dimensional linear stochastic switched systems

Guojie Zheng; Taige Wang; Guojie Zheng; Taige Wang

doi:10.3934/math.20231257

AIMS Mathematics

2023, Volume 8, Issue 10: 24663-24680. doi: 10.3934/math.20231257

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Research article

The moment exponential stability of infinite-dimensional linear stochastic switched systems

Guojie Zheng ^{1
,
,},
Taige Wang ²

1.
College of Digital Technology and Engineering, Ningbo University of Finance & Economics, Ningbo 315175, China
2.
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA

Received: 10 May 2023 Revised: 14 July 2023 Accepted: 07 August 2023 Published: 21 August 2023
MSC : 60H30, 93E15

This paper studies the 2nd-moment exponential stability of a class of infinite-dimensional linear stochastic switched systems comprising two unstable subsystems. We first construct an algebraic sufficient condition on the existence of multiple Lyapunov functions. Then, two switching strategies are designed to stabilize infinite-dimensional linear stochastic switched systems in terms of the multiple Lyapunov function method. Moreover, the system possesses good robust stability of the switching time with our switching strategies.
- infinite-dimensional stochastic switched systems,
- stability analysis,
- multiple Lyapunov function,
- Itô formula
Citation: Guojie Zheng, Taige Wang. The moment exponential stability of infinite-dimensional linear stochastic switched systems[J]. AIMS Mathematics, 2023, 8(10): 24663-24680. doi: 10.3934/math.20231257

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Abstract

This paper studies the 2nd-moment exponential stability of a class of infinite-dimensional linear stochastic switched systems comprising two unstable subsystems. We first construct an algebraic sufficient condition on the existence of multiple Lyapunov functions. Then, two switching strategies are designed to stabilize infinite-dimensional linear stochastic switched systems in terms of the multiple Lyapunov function method. Moreover, the system possesses good robust stability of the switching time with our switching strategies.

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