Weighted input to state stability for delay coupled systems on networks

In this paper, the weighted input to state stability (ISS) for a general delay coupled system on networks (DCSNs) is investigated. A simple criterion ensuring the weighted ISS of DCSNs is established, by applying Lyapunov method. A systematic method for constructing Lyapunov function of the DCSNs is provided by graph theory. To make the results more understandable, we apply them to a coupled oscillators with control input, and sufficient conditions for weighted ISS are obtained. Finally, a numerical example demonstrates effectiveness and feasibility of the obtained results.