Stability of Asynchronous Networked Control Systems with Probabilistic Clocks

Abstract: This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as deterministic sampling, jitter, and transmission times of packet dropping networks. Moreover, the stability theory can be applied to an arbitrary number of clocks with different distributions, operating asynchronously. The paper gives Lyapunov-type sufficient conditions for stochastic stability of nonlinear networked systems. For linear systems, the paper gives necessary and sufficient conditions for exponential mean square stability, based on linear matrix inequalities. In both the linear and nonlinear cases, the Lyapunov inequalities are constructed from a simple linear combination of the classical inequalities from continuous and discrete time. Crucially, the stability theorems only depend on the mean sampling intervals. Thus, they can be applied with only limited statistical information about the clocks. The Lyapunov theorems are then applied to systems with multirate sampling, asynchronous communication, delays, and packet losses.