The behavior of incrementally stable discrete time systems

摘要

This paper focus on the behavior analysis of incrementally bounded (Lipschitz continuous) systems on l(p) with p is an element of [1, infinity). We first establish the properties of the motions, which are associated with all inputs inside l(p)(e) with respect to a modification of the initial condition. As a matter of fact, under some minimality properties of the state-space realization of the system, we prove the Lyapunov stability of all unperturbed motions. As a second point, we investigate the properties of the motions obtained when the input is perturbed, either by perturbations which go to zero at the infinity, or by perturbations with a bounded magnitude. All these results are obtained through the reformulation of the incremental boundedness of a system in terms of the dissipativity of an associated fictitious system. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 15]