Stabilization of Highly Nonlinear Stochastic Coupled Systems via Periodically Intermittent Control

Abstract

This article considers the stabilization of highly nonlinear stochastic coupled systems (HNSCSs) with time delay via periodically intermittent control. This article is motivated by that known differential inequalities to deal with periodically intermittent control do not work for HNSCSs, since the coefficients of the system do not satisfy the linear growth condition. In order to cope with this problem, a novel Halanay-type inequality is established to handle periodically intermittent control, which generalizes previous results. Then, based on this differential inequality, the graph theory, and the Lyapunov method, two main theorems are shown, whose conditions indicate how the control duration, the control gain, and the coupling strength affect the realization of the stability. Then, the theoretical results are applied to the modified van der Pol–Duffing oscillators. Finally, corresponding simulation results are presented to illustrate the effectiveness of the theoretical results.