Input-to-state stability of stochastic nonlinear system with delayed impulses

Linni Li; Jin-E Zhang; Linni Li; Jin-E Zhang

doi:10.3934/mbe.2024098

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 2: 2233-2253. doi: 10.3934/mbe.2024098

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Input-to-state stability of stochastic nonlinear system with delayed impulses

Linni Li ,
Jin-E Zhang ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Academic Editor: Xiaodi Li

Received: 29 November 2023 Revised: 02 January 2024 Accepted: 04 January 2024 Published: 12 January 2024

Stochastic input-to-state stability (SISS) of the stochastic nonlinear system has received extensive research. This paper aimed to investigate SISS of the stochastic nonlinear system with delayed impulses. First, when all subsystems were stable, using the average impulsive interval method and Lyapunov approach, some theoretical conditions ensuring SISS of the considered system were established. The SISS characteristic of the argumented system with both stable and unstable subsystems was also discussed, then the stochastic nonlinear system with multiple delayed impulse jumps was considered and SISS property was explored. Additionally, it should be noted that the Lyapunov rate coefficient considered in this paper is positively time-varying. Finally, several numerical examples confirmed validity of theoretical results.
- stochastic nonlinear system,
- input-to-state stability,
- delayed impulses,
- multiple jumps
Citation: Linni Li, Jin-E Zhang. Input-to-state stability of stochastic nonlinear system with delayed impulses[J]. Mathematical Biosciences and Engineering, 2024, 21(2): 2233-2253. doi: 10.3934/mbe.2024098

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Abstract

Stochastic input-to-state stability (SISS) of the stochastic nonlinear system has received extensive research. This paper aimed to investigate SISS of the stochastic nonlinear system with delayed impulses. First, when all subsystems were stable, using the average impulsive interval method and Lyapunov approach, some theoretical conditions ensuring SISS of the considered system were established. The SISS characteristic of the argumented system with both stable and unstable subsystems was also discussed, then the stochastic nonlinear system with multiple delayed impulse jumps was considered and SISS property was explored. Additionally, it should be noted that the Lyapunov rate coefficient considered in this paper is positively time-varying. Finally, several numerical examples confirmed validity of theoretical results.

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