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IMA Journal of Mathematical Control and Information 1999 16(1):23-41; doi:10.1093/imamci/16.1.23
© 1999 by Institute of Mathematics and its Applications
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Stability of discrete nonlinear systems under novanishing pertuabations: application to a nonlinear model-matching problem

CÉSAR CRUZ-HERNÁNDEZ{dagger}, JOAQUÍN ALVAREZ-GALLEGOS and RAFAEL CASTRO-LINARES{ddagger}

Electronics & Telecommunications Department CICESE, P. O. Box 434944, San Diego, CA 92143-4944, USA
Department of Electrical Engineering CINVESTAV, P. O. Box 14-740, 07000, Mexico, D. F., Mexico
{dagger} E-mail: ccruz{at}cicese.mx
{ddagger} E-mail: rcastro{at}ctrl.cinvestav.mx

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.

Keywords: Discrete nonlinear systems; perturbed systems; model-matching problem; stability robustness.


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