Robust asymptotic controllability under time-varying perturbations

L. Grüne: Robust asymptotic controllability under time-varying perturbations
Stochastics & Dynamics 4, 297 - 316, 2004

DOI: 10.1142/S0219493704001085
Keywords: robust controllability; time-varying perturbation; discretization
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We investigate the effect of time-varying perturbations on the dynamical behavior of nonlinear control systems. More specifically, we study the effect of such perturbations on the controlled equivalent of asymptotically stable sets, i.e., asymptotically controllable sets. In the first part of this paper we illustrate by a simple example how different types of perturbations affect this dynamical behavior and use concepts from dynamical game theory in order to identify classes of perturbations which allow to model the effects of numerical discretization errors both in time and space. In the second part we introduce appropriate robustness properties and prove that these are inherent properties for asymptotically controllable sets under these classes of perturbations.

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