Input-to-state stability for discrete time-delay systems via the Razumikhin technique

This paper aims to study the problem of input-to-state stability (ISS) for discrete time-delay systems. By employing the Razumikhin technique and suitable Lyapunov functions, backward and forward Razumikhin-type ISS theorems, that guarantee the global ISS, global asymptotic ISS and global exponential ISS for general discrete time-delay systems are established. Moreover, Razumikhin-type global exponential ISS theorems give the estimation of the convergence speed. As an application, the Razumikhin-type exponential ISS result is used to derive exponential ISS criteria for a class of interconnected discrete systems with coupling time-delays and disturbance inputs. Finally, examples are given to illustrate the results.