Delay independent asymptotic stability of n-dimensional systems of Roesser´s type with state delays by means of memoryless state feedback controller

This paper deals with the problem of robust stabilization of n-dimensional discrete time systems with state delays by means of a memoryless state feedback controller. First, a sufficient stability condition on the grounds of the Lyapunov functional is examined. Next, the disturbance rejection issue is discussed. Finally, it is presented a memoryless state feedback controller that yields an asymptotically stable system with disturbance rejection characteristic. The conditions are independent of the delays and are formulated in the linear matrix inequality (LMI) settings.