On Asymptotic Stabilizability of Discrete-time Linear Systems with Delayed Input

This paper examines the asymptotic stabilizability of discrete-time linear systems with delayed input. By explicit construction of stabilizing feedback laws, it is shown that a stabilizable and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open loop system is not exponentially unstable (i.e., all the open loop poles are on or inside the unit circle.) It is further shown that such a system, when subject to actuator saturation, is semi-globally asymptotically stabilizable by linear state or output feedback.