Stability of nonlinear systems with multi-delayed random impulses: Average estimation and delay approach

Yao Lu; Dehao Ruan; Quanxin Zhu; Yao Lu; Dehao Ruan; Quanxin Zhu

doi:10.3934/math.2025982

AIMS Mathematics

2025, Volume 10, Issue 9: 22075-22091. doi: 10.3934/math.2025982

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Stability of nonlinear systems with multi-delayed random impulses: Average estimation and delay approach

Yao Lu ^1,2,
Dehao Ruan ^{1,2
,
,},
Quanxin Zhu ^{2
,
,}

1.
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, China
2.
MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410081, China

Received: 04 August 2025 Revised: 11 September 2025 Accepted: 15 September 2025 Published: 23 September 2025
MSC : 34K50, 90B15, 93D20

This study focuses on analyzing the exponential stability in the pth moment for a class of random impulsive delayed nonlinear systems (RIDNSs) influenced by multiple randomly delayed impulses. The underlying continuous-time dynamics are governed by random delay differential equations subjected to stochastic perturbations modeled as second-order moment processes. To establish new stability conditions, we employ tools such as the average random impulsive estimation (ARIE), average impulsive delay (AID), average delay time (ADT), and Lyapunov-based techniques. The developed criteria are applicable not only to inherently stable or unstable systems, but also to scenarios where impulses with stabilizing and destabilizing effects appear simultaneously. Several illustrative examples are included to verify the applicability and advantages of the proposed approach.
- random impulsive delayed nonlinear systems,
- exponential stability,
- average random impulsive estimation,
- average-delay impulse
Citation: Yao Lu, Dehao Ruan, Quanxin Zhu. Stability of nonlinear systems with multi-delayed random impulses: Average estimation and delay approach[J]. AIMS Mathematics, 2025, 10(9): 22075-22091. doi: 10.3934/math.2025982

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Abstract

This study focuses on analyzing the exponential stability in the pth moment for a class of random impulsive delayed nonlinear systems (RIDNSs) influenced by multiple randomly delayed impulses. The underlying continuous-time dynamics are governed by random delay differential equations subjected to stochastic perturbations modeled as second-order moment processes. To establish new stability conditions, we employ tools such as the average random impulsive estimation (ARIE), average impulsive delay (AID), average delay time (ADT), and Lyapunov-based techniques. The developed criteria are applicable not only to inherently stable or unstable systems, but also to scenarios where impulses with stabilizing and destabilizing effects appear simultaneously. Several illustrative examples are included to verify the applicability and advantages of the proposed approach.

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