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Exponential input-to-state stabilization of stochastic nonlinear reaction–diffusion systems with time-varying delays and exogenous disturbances via boundary control

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Abstract

The boundary stabilization problem of stochastic nonlinear reaction–diffusion systems (SNRDSs) with time-varying delay, exogenous disturbance, and boundary controller is addressed. To solve this problem, the Neumann boundary condition introduces a state feedback controller. By employing Lyapunov method, Wirtinger’s inequality, and linear matrix inequality (LMI) method, sufficient criteria are obtained to guarantee the SNRDSs achieve exponential input-to-state stabilization. These criteria are used to analyze the effects of boundary controllers, reaction–diffusion, time-varying delays, and exogenous disturbances on exponential input-to-state stability. Furthermore, the obtained results are successfully applied to stochastic reaction–diffusion Hopfield neural networks (SRDHNNs). At last, the effectiveness and superiority of the proposed boundary controllers are illustrated by numerical simulations.

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Authors and Affiliations

  1. Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, Tamil Nadu, 600089, India

    V. Gokulakrishnan & R. Srinivasan

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  1. V. Gokulakrishnan
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  2. R. Srinivasan
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Correspondence to R. Srinivasan.

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Communicated by Nadhir Messai.

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Gokulakrishnan, V., Srinivasan, R. Exponential input-to-state stabilization of stochastic nonlinear reaction–diffusion systems with time-varying delays and exogenous disturbances via boundary control. Comp. Appl. Math. 42, 308 (2023). https://doi.org/10.1007/s40314-023-02447-y

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