Improved stability conditions for sampled data systems with jitter

Abstract

This paper is concerned with the discrete time approach for the robust stability of sampled-data systems (Aström and Wittenmark [1997]) with sampling jitter. We assume that the sampling is unknown, time-varying and bounded in a given interval. Several discrete-time approaches exist in the literature. The intention of the paper is to clearly analyse the relations between them and to indicate the sources of conservatism. It will point out that the different existing models can be studied in the framework of difference inclusions with polytopic and norm bounded components. Furthermore, it will show how to reduce the conservatisms by using recent stability analysis tools based on Lyapunov functions with non-monotonic Lyapunov increment. The idea is to improve the stability conditions by considering α-samples variations, i.e. ΔαV(xk) = V(xk+α) — V(xk) < 0. Numerical examples illustrate the effectiveness of the approach.