A note on stability and stabilization of discrete-time systems with time-varying delay

This paper is concerned with the stability and stabilization problem of the discrete-time systems with time-varying delay. Using “lifting” technique, a discrete-time system with time-varying delay is transformed into a switched system. On the basis of theories of switched systems, some necessary and sufficient stability conditions are obtained. However, these conditions are hard to check. Using the switched Lyapunov function approach, some equivalent sufficient stability conditions are developed. Based on these conditions, a state feedback controller with varying gains is designed. Numerical examples are given to show the effectiveness of the proposed method.