The behaviour of incrementally stable discrete time systems

This paper focus on the behaviour analysis of incrementally bounded (Lipschitz continuous) systems on l_p with p∈[1,∞). 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. In fact, under some minimality properties of the state-space realization of the system, we prove the Lyapunov stability of all unperturbed motions. Next, 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