Impulsive effects on stabilization of stochastic nonlinear reaction-diffusion systems with time delays and boundary feedback control

Abstract

In this paper, we investigate the stabilization of stochastic nonlinear impulsive reaction-diffusion systems (SNIRDSs) with time delays and boundary feedback control via average impulsive interval approach. Boundary feedback control strategy are designed to stabilization of SNIRDSs. By constructing a Lyapunov-Krasovskii functional (LKF), and using Wirtinger's inequality, Gronwall inequality, average impulsive interval approach, sufficient conditions are derived to guarantee the finite-time stability (FTS) of proposed systems. We investigate the stabilization results by designing the control gain matrices for boundary feedback controller. The criterions are expressed in terms of linear matrix inequalities (LMIs) that can be verified by Matlab LMI toolbox. Finally, numerical example are given to verify the efficiency and superiority of proposed stabilization criterions.

Event-triggered controller on practically exponential input-to-state stabilization of stochastic reaction-diffusion neural networks and its application to image encryption

“…Lemma 2 [28] There exist real matrices Υ 1 , Υ 2 , and a positive definite matrix W such that the following inequality is holds:…”

“…These behaviors are modeled by partial differential equations (PDE). However, the diffusion effects inevitable in NNs while electrons move through unsymmetrical electromagnetic fields [28][29][30][31].…”