Practical stability and controllability for nonlinear discrete time-delay systems

In this paper we study the practical asymptotic stability for a class of discrete-time time-delay systems via Razumikhin-type Theorems. Further estimations of the solution boundary and arrival time of the solution are also investigated based on practical stability. In addition, the proposed theorems are used to analyze the practical controllability of a general class of nonlinear discrete systems with input time delay. Some easy testing criteria for the uniform practical asymptotical stability are derived via Lyapunov function and Razumikhin technique. Finally a numerical example is given to illustrate the effectiveness of the proposed results.