Stabilization of Highly Nonlinear Stochastic Time-Varying Coupled Systems via Aperiodically Intermittent Control

Abstract

Highly non-linear stochastic time-varying coupled systems are first considered in which the coupling structure is time-variant. It is worth pointing out that aperiodically intermittent control (AIC) is considered to achieve the stability of highly non-linear stochastic time-varying coupled systems. Since the existing research methods for processing AIC are not suitable for stochastic highly non-linear systems, a new Halanay-type differential inequality with higher-order nonlinear terms that extends the existing Halanay-type differential inequalities is established. Then, with the help of the Lyapunov method, some techniques of inequalities and the graph theory, two stabilization criteria are presented to guarantee the exponential stabilization for highly non-linear stochastic time-varying coupled systems. Finally, as an application of our results, the modified time-varying coupled Van der Pol-Duffing oscillators are studied via AIC with numerical simulations provided.