Stability of discrete nonlinear systems under nonvanishing perturbations: application to a nonlinear model-matching problem

摘要

A stability analysis of discrete-time nonlinear systems subjected to a class of nonvanishing perturbations is presented. It is shown that, if the equilibrium point of the unperturbed system is uniformly asymptotically or exponentially stable, then the state trajectories are ultimately bounded if some conditions on the perturbations are satisfied. A region with guaranteed stability for the perturbed system is also given. The results obtained are applied to the model-matching problem associated with a perturbed discrete-time nonlinear system.