Fixed/Prescribed stability criterions of stochastic system with time-delay

Yabo Zhao; Huaiqin Wu; Yabo Zhao; Huaiqin Wu

doi:10.3934/math.2024701

AIMS Mathematics

2024, Volume 9, Issue 6: 14425-14453. doi: 10.3934/math.2024701

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Research article

Fixed/Prescribed stability criterions of stochastic system with time-delay

Yabo Zhao ^,,
Huaiqin Wu

School of Science, Yanshan University, Qinhuangdao 066001, China

Received: 02 March 2024 Revised: 04 April 2024 Accepted: 12 April 2024 Published: 22 April 2024
MSC : 93D05, 93E03

In this paper, the fixed/prescribed-time stability issues were considered for stochastic systems with time delay. First, some new fixed-time stability and prescribed-time stability criteria for stochastic systems with delay and multi-delay were established. Second, based on the new fixed/prescribed stability criteria, the fixed-time stabilization of the stochastic system with time-delay and the prescribed-time stabilization of the stochastic reaction-diffusion system with multi-delay were investigated, respectively. Third, two new fixed/prescribed-time delay-independent control mechanisms were designed. The primary advantage of the innovative fixed/prescribed-time controller lies in its independence from delayed states. This makes the controller applicable to systems with unknown delays. Finally, three numerical examples were provided to illustrate the feasibility of the stated theoretical results.
- fixed-time stability,
- prescribed-time stability,
- stochastic system,
- time-delay
Citation: Yabo Zhao, Huaiqin Wu. Fixed/Prescribed stability criterions of stochastic system with time-delay[J]. AIMS Mathematics, 2024, 9(6): 14425-14453. doi: 10.3934/math.2024701

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Abstract

In this paper, the fixed/prescribed-time stability issues were considered for stochastic systems with time delay. First, some new fixed-time stability and prescribed-time stability criteria for stochastic systems with delay and multi-delay were established. Second, based on the new fixed/prescribed stability criteria, the fixed-time stabilization of the stochastic system with time-delay and the prescribed-time stabilization of the stochastic reaction-diffusion system with multi-delay were investigated, respectively. Third, two new fixed/prescribed-time delay-independent control mechanisms were designed. The primary advantage of the innovative fixed/prescribed-time controller lies in its independence from delayed states. This makes the controller applicable to systems with unknown delays. Finally, three numerical examples were provided to illustrate the feasibility of the stated theoretical results.

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