Act-and-wait control of discrete systems with random delays

This paper addresses the stabilization of discrete-time linear systems with random delays, which is a common problem in networked control systems. The delays are assumed to be bounded and longer than a sampling time unit. We apply the act-and-wait control concept to stabilize the system: the controller is on for one sampling period (act) and off for some sampling periods (wait). If the waiting period is longer than the maximum delay in the feedback, then the stability can be described by finite number of eigenvalues. Although the closed-loop stability of the stochastic system with the act-and-wait controller is characterized by the Lyapunov exponent of infinite random matrix products, the dimension of these matrices is finite, which results in a significant reduction of computational complexity. The applicability of this method is demonstrated in a simple example, where we compare deterministic stability with the Lyapunov exponent based results.