Semi-Global Stabilization of Discrete-Time Linear Systems Subject to Infinite Distributed Input Delays and Actuator Saturations

The semi-global stabilization problem of discrete-time systems subject to infinite distributed input delays and actuator saturations is investigated in this article. This article develops two low-gain feedback control laws for two types of systems, respectively. It is shown that the resulting system is semi-globally exponentially stabilized. Our results include those existing results on systems subject to only input saturations and systems subject to bounded delays and input saturations as special cases. Compared with existing results on infinite delays and actuator saturations, this article develops a more accurate scaling utilizing a more general framework. Furthermore, a novel converse Lyapunov theorem for discrete-time linear infinite-delayed systems and a novel stability analysis theorem for perturbed discrete-time linear infinite-delayed systems are developed to handle the nonlinearity induced by saturations. Finally, this article provides two numerical examples to illustrate the effectiveness of the developed theorems.