Stabilization of Stochastic Uncertain Complex-Valued Delayed Networks via Aperiodically Intermittent Nonlinear Control

This paper concerns the stabilization problem of stochastic uncertain complex-valued delayed networks (SUCVDNs) via aperiodically intermittent nonlinear control. It is worth noting that the intermittent control is aperiodic and nonlinear. As a special case, when each control width tends to zero, intermittent control becomes impulsive control. Hence, the stabilization problem of SUCVDNs via impulsive control is also studied. The main method is the combination of the Lyapunov method and Kirchhoff’s matrix tree theorem in graph theory, which does not require us to solve any linear matrix inequalities. Different from previous results on complex-valued system, we consider the complex-valued system on complex space directly by using complex version Itô’s formula and (conjugate)
${\mathbb {R}}$
derivative. Then we give some sufficient criteria, which have a close relationship with the control interval and the topological structure of the considered network. The main results are applied to a class of stochastic complex-valued coupled oscillators, and numerical examples are also presented to show the effectiveness of the control strategies.