Stabilization of some specific stochastic Reaction Diffusion Systems with Time Varying delays

Abstract

Successful applications of stochastic reaction-diffusion systems (SRDSs) have been newline achieved in various fields such as biological systems, image processing, secure communication, newline pattern recognition, and so on. However, such applications are highly dependent on the newline dynamic behavior of the adopted systems and its stability. Therefore, the motivation for this newline thesis is to study the stability and stabilization problem of SRDSs with time-varying delays. newline Firstly, the finite-time guaranteed cost control problem of stochastic nonlinear switched systems newline (SNSSs) with time-varying delays and reaction-diffusion is investigated using the Lyapunov newline method, Neumann boundary conditions, and the average dwell-time approach. Secondly, newline the exponential input-to-state stabilization problem of stochastic nonlinear reaction-diffusion newline systems (SNRDSs) with time-varying delays and exogenous disturbances is studied using newline the ideas of boundary control, Wirtinger s inequality, and linear matrix inequality. Thirdly, newline the practically exponential input-to-state stabilization problem of stochastic reaction-diffusion newline delayed Cohen-Grossberg neural networks (SRDDCGNNs) with distributed and boundary newline external disturbances is studied using an event-triggered control approach. Finally, the finite newlinetime boundary stabilization problem of stochastic delayed reaction-diffusion Cohen-Grossberg newline BAMneural networks (SDRDCGBAMNNs) with impulsive effects is studied using an average newline impulsive interval approach. Numerical examples with simulation results are given in each newline chapter to demonstrate the efficiency and applicability of the proposed results newline