Global exponential stability for coupled retarded systems on networks: A graph-theoretic approach

• A theoretical framework for the construction of Lyapunov function is derived.
• Graph theory and the Lyapunov method are used in this article.
• Some sufficient conditions of the global exponential stability are given.

In this paper, some coupled retarded systems on networks (CRSNs) are studied. Applying the idea of Razumikhin method and Mirchhoff’s matrix tree theorem, the sufficient conditions for global exponential stability of the CRSNs are obtained. Finally, an example of coupled retarded oscillator system on networks is given to illustrate the advantages of our results.