Stability analysis of discrete-time systems with constrained delays

This paper addresses the asymptotic stability issue of discrete-time multiple time-varying delays systems with given delay digraph. By using the switching transformation approach, the discrete-time system with multiple time-varying delays is transformed into an equivalent switched system. Different delays correspond to the different switching signals, and the stability analysis of the delay system is turned into that of a switched system. It is the first time that switched homogeneous Lyapunov function approach is applied to constrained delay systems. A sufficient condition is established to check the stability of the considered system, and the monotonicity property of the condition is provided. Finally, an example is listed to illustrate the theoretical results.