Stabilization of nonlinear hybrid stochastic time-delay neural networks with Lévy noise using discrete-time feedback control

Tian Xu; Ailong Wu; Tian Xu; Ailong Wu

doi:10.3934/math.20241317

AIMS Mathematics

2024, Volume 9, Issue 10: 27080-27101. doi: 10.3934/math.20241317

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Stabilization of nonlinear hybrid stochastic time-delay neural networks with Lévy noise using discrete-time feedback control

Tian Xu ,
Ailong Wu ^,

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

Received: 26 July 2024 Revised: 05 September 2024 Accepted: 12 September 2024 Published: 19 September 2024
MSC : 93C30

This paper aims to formulate a class of nonlinear hybrid stochastic time-delay neural networks (STDNNs) with Lévy noise. Specifically, the coefficients of networks grow polynomially instead of linearly, and the time delay of given neural networks is non-differentiable. In many practical situations, nonlinear hybrid STDNNs with Lévy noise are unstable. Hence, this paper uses feedback control based on discrete-time state and mode observations to stabilize the considered nonlinear hybrid STDNNs with Lévy noise. Then, we establish stabilization criteria of $ H_{\infty} $ stability, asymptotic stability, and exponential stability for the controlled nonlinear hybrid STDNNs with Lévy noise. Finally, a numerical example illustrating the usefulness of theoretical results is provided.
- stochastic time-delay neural networks,
- highly nonlinear,
- Lévy noise,
- discrete-time state and mode,
- stabilization
Citation: Tian Xu, Ailong Wu. Stabilization of nonlinear hybrid stochastic time-delay neural networks with Lévy noise using discrete-time feedback control[J]. AIMS Mathematics, 2024, 9(10): 27080-27101. doi: 10.3934/math.20241317

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Abstract

This paper aims to formulate a class of nonlinear hybrid stochastic time-delay neural networks (STDNNs) with Lévy noise. Specifically, the coefficients of networks grow polynomially instead of linearly, and the time delay of given neural networks is non-differentiable. In many practical situations, nonlinear hybrid STDNNs with Lévy noise are unstable. Hence, this paper uses feedback control based on discrete-time state and mode observations to stabilize the considered nonlinear hybrid STDNNs with Lévy noise. Then, we establish stabilization criteria of $ H_{\infty} $ stability, asymptotic stability, and exponential stability for the controlled nonlinear hybrid STDNNs with Lévy noise. Finally, a numerical example illustrating the usefulness of theoretical results is provided.

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