Razumikhin method conjoined with graph theory to input-to-state stability of coupled retarded systems on networks

This paper is concerned with input-to-state stability (ISS) of coupled retarded systems on networks (CRSNs). By incorporating Razumikhin method with generalized Kirchhoff's Matrix Tree Theorem, sufficient conditions are established to guarantee ISS of CRSNs. For the convenience of application, sufficient conditions in the form of coefficients are also obtained. What is more, a sufficient criterion on ISS of the coupled retarded oscillators system on networks is derived. Finally, as an illustration, a numerical example is given to demonstrate the effectiveness of the theoretical results.