Stabilization of discrete-time linear systems with infinite distributed input delays

This paper investigates the stabilization problem of discrete-time linear systems with infinite distributed input delays. A novel framework is adopted to analyze the stability of the concerned systems. Under this framework, two truncated predictor feedback controllers are developed for two classes of discrete-time linear systems with infinite distributed input delays via the low gain method respectively. It is shown that under the designed controllers, those two classes systems are globally exponentially stable. To the best of our knowledge, this is the first time that the stabilization problem of discrete-time linear systems with infinite distributed input delays is considered. Two simulation examples are provided to illustrate the effectiveness of the proposed controllers.