A graph-theoretic method to stabilize the delayed coupled systems on networks based on periodically intermittent control

This paper mainly focus on the exponential stabilization problem of coupled systems on networks with mixed time-varying delays. Periodically intermittent control is used to control the coupled systems on networks with mixed time-varying delays. Moreover, based on the graph theory and Lyapunov method, two different kinds of stabilization criteria are derived, which are in the form of Lyapunov-type theorem and coefficients-type criterion, respectively. These laws reveal that the stability has a close relationship with the topology structure of the networks. In addition, as a subsequent result, a decision theorem is also presented. It is straightforward to show the stability of original system can be determined by that of modified system with added absolute value into the coupling weighted-value matrix. Finally, the feasibility and validity of the obtained results are demonstrated by several numerical simulation figures.