New Results on the Stability of Discrete-Time Systems and Applications to Control Problems

Abstract

The aim of this article is to present some new stability sufficient conditions for discrete-time nonlinear systems. It shows how to use nonnegative semi-definite functions as Lyapunov functions instead of positive definite ones for studying the stability of a given system. Several examples and some applications to control theory are presented to illustrate the various theorems. © 1998 Academic Press.