General approach to stability and stabilization for a class of uncertain discrete non-linear systems

Abstract

This paper presents a general and unified approach to the problem of stability and stabilization for uncertain discrete-time systems which may be both non-linear and time-varying. General stability conditions based on the principle of contraction mapping are recalled and used to formulate unified stability conditions and stabilization problem for the uncertain system under consideration. For two typical cases (additive uncertainty and multiplicative uncertainty) and three forms of uncertainties, a set of sufficient stability conditions is presented. Some of them are compared with the related conditions described in the literature.