Graph-theoretic approach to exponential synchronization of coupled systems on networks with mixed time-varying delays

In this paper, the issue of exponential synchronization for coupled systems on networks with mixed time-varying delays is concerned. An approach combining Kirchhoff's matrix tree theorem in graph theory with Lyapunov method and periodically intermittent control is taken to investigate the problem. This method is different from the corresponding previous works. Two different kinds of synchronization conditions in the form of Lyapunov-type theorem and coefficients-type criterion are derived. They both reveal synchronization has a close relation with the topology structure of the network. Finally, the feasibility and effectiveness of the proposed method are illustrated by several numerical simulation figures.