Asymptotic stability of impulsive stochastic switched system with double state-dependent delays and application to neural networks and neural network-based lecture skills assessment of normal students

Yueli Huang; Jin-E Zhang; Yueli Huang; Jin-E Zhang

doi:10.3934/math.2024011

AIMS Mathematics

2024, Volume 9, Issue 1: 178-204. doi: 10.3934/math.2024011

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Asymptotic stability of impulsive stochastic switched system with double state-dependent delays and application to neural networks and neural network-based lecture skills assessment of normal students

Yueli Huang ,
Jin-E Zhang ^,

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

Received: 23 August 2023 Revised: 12 November 2023 Accepted: 16 November 2023 Published: 27 November 2023
MSC : 92B20, 93C30

This article investigates the stability problem of impulsive stochastic switched systems with double state-dependent delays. In the designed system, unstable and stable impulses are taken into consideration, respectively, and they do not need to function simultaneously with switching behavior. Additionally, two new ideas, i.e., mode-dependent switching density and mode-dependent impulsive density, are developed. Based on the Lyapunov function method and comparison principle, the asymptotic stability criteria for an impulsive stochastic switched system with state-dependent delays are given. Moreover, the application of theoretical results to neural networks and the neural network-based lecture skills assessment of normal students is analyzed. Finally, two numerical examples are provided to illustrate the effectiveness and reliability of the theoretical criteria.
- switched system,
- hybrid model,
- state-dependent delay,
- mode-dependent impulsive density,
- mode-dependent switching density
Citation: Yueli Huang, Jin-E Zhang. Asymptotic stability of impulsive stochastic switched system with double state-dependent delays and application to neural networks and neural network-based lecture skills assessment of normal students[J]. AIMS Mathematics, 2024, 9(1): 178-204. doi: 10.3934/math.2024011

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Abstract

This article investigates the stability problem of impulsive stochastic switched systems with double state-dependent delays. In the designed system, unstable and stable impulses are taken into consideration, respectively, and they do not need to function simultaneously with switching behavior. Additionally, two new ideas, i.e., mode-dependent switching density and mode-dependent impulsive density, are developed. Based on the Lyapunov function method and comparison principle, the asymptotic stability criteria for an impulsive stochastic switched system with state-dependent delays are given. Moreover, the application of theoretical results to neural networks and the neural network-based lecture skills assessment of normal students is analyzed. Finally, two numerical examples are provided to illustrate the effectiveness and reliability of the theoretical criteria.

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