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

Volume 28, Issue 4, pp 350--362 http://dx.doi.org/10.22436/jmcs.028.04.04

Publication Date: July 26, 2022 Submission Date: April 07, 2022 Revision Date: April 21, 2022 Accteptance Date: May 20, 2022

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Authors

V. Gokulakrishnan - Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai-600 089, Tamilnadu, India. R. Srinivasan - Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai-600 089, Tamilnadu, India.

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.

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Keywords

• Stochastic nonlinear systems
• reaction-diffusion terms
• impulsive effects
• boundary feedback control
• average impulsive interval approach

MSC

•  93C10
•  93E03
•  93E15

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