Stability Analysis of Discrete-Time Coupled Systems on Networks with Time-Varying Delay

This paper is concerned with the global stability problem for discrete-time coupled systems on networks (DTCSN) with time-varying delay. Based on graph-theoretical technique and Lyapunov method, an effective method is given to construct a global Lyapunov function for the DTCSN. Then two kinds of novel sufficient criteria are obtained which show that both the topological structure of the underlying network and the upper and lower bounds of time-varying delay do great influence on the stability of DTCSN. Subsequently, the theoretical results are applied to a class of discrete-time coupled oscillators, which is derived by Euler method. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.