For these reasons, we will study the stability problem of DCSNs under periodically intermittent control, the k-th vertex system is constructed as follows:
In this section, with the help of graph theory and Lyapunov function method as well as periodically intermittent control, two kinds of exponential stability criteria for DCSNs are established in the form of Lyapunov function and the coefficients of DCSNs.
Hence, Assumption 1 provides a restriction for weighted matrix [([[delta].sub.kh]).sub.lxl] to guarantee the stability of DCSNs.
Hence, based on the graph-theoretic approach, a new method is presented by utilizing the vertex-Lyapunov function [V.sub.k], which is first applied to analyze the exponential stability of DCSNs under periodically intermittent control.
It is worth pointing that, by using some results in graph theory, a global Lyapunov function V of DCSNs is successfully constructed via the vertex-Lyapunov functions [V.sub.k] and the topology property of systems.