Intermittent Control to Stabilization of Stochastic Highly Non-Linear Coupled Systems With Multiple Time Delays.

Abstract

This article investigates the stabilization of stochastic highly non-linear coupled systems (SHNCSs) with multiple time delays by using periodically intermittent control (PIC). It is worth noting that coefficients in SHNCSs dissatisfy the linear growth condition, which weakens the previous stability conditions. In addition, PIC and multiple time delays are first introduced into the study of highly nonlinear systems, which leads to the existing methods being inapplicable to investigate the stability of SHNCSs with multiple time delays. Therefore, a novel Halanay-type differential inequality is established, which can be employed to deal with highly nonlinear systems with PIC. Based on the Lyapunov method, the graph theory, and the novel differential inequality, SHNCSs with multiple time delays are first studied, and stability criteria are presented. Next, the theoretical results can be applied to modified FitzHugh-Nagumo models. At last, a numerical example is presented to show the effectiveness of our results.