Numeric and Analytic Investigations of Mean-Square Exponential Stability for Stochastically Timed Systems

This paper is motivated by the problems posed in feedback control design when actuators, sensors, and/or computational nodes connect via unreliable or unpredictable communications channels. In these cases, there is a degree of stochastic uncertainty to the timing of the system’s discretizing elements, such as digital-to-analog converters. Several theorems related to the stability of non-uniformly sampled discrete dynamical systems have recently been proposed; here we examine through numeric investigation the characteristics of systems which are mean square exponentially stable (MSES). In particular we present a method to compute the range of mean and variance that a nonuniformly discretized feedback control system may tolerate while remaining MSES. Several examples are presented.