Asymptotical stability of stochastic delayed time-varying systems with stochastic delayed impulses

Zhaoli Jia, Xiang Li, Qian Cui and Lulu Li

International Journal of Systems Science, 2025, vol. 56, issue 8, 1662-1674

Abstract: This paper investigates the asymptotical stability of stochastic delayed time-varying systems (SDTVS) with stochastic delayed impulses, which is a challenging and important problem in impulsive control theory. We utilise the impulsive density function (IDF) without linear constraints to estimate the number of impulses and the size of impulsive delay, which can better capture the impulsive effects than the conventional average impulsive interval (AII). We also relax the constraints between impulsive delay and the delay in the continuous dynamics by comparing their sizes, rather than requiring them to satisfy certain inequalities. We employ the comparison principle and the Razumikhin condition to derive Razumikhin-type stability results for our systems. We illustrate our results with two numerical examples that demonstrate their effectiveness and applicability.

Date: 2025
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DOI: 10.1080/00207721.2024.2429024

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