Abstract
We study nonlinear systems with an asymptotically stable fixed point subject to time-varying perturbations that do not perturb the fixed point. Based on linearization theory we show that in discrete time the linearization completely determines the local robustness properties at exponentially stable fixed points of nonlinear systems. In the continuous time case we present a counterexample for the corresponding statement. Sufficient conditions for the equality of the stability radii of nonlinear respective linear systems are given. We conjecture that they hold on an open and dense set.
Research supported by the European Nonlinear Control Network.
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Wirth, F. (2002). A Linearization Principle for Robustness with Respect to Time-Varying Perturbations. In: Colonius, F., Grüne, L. (eds) Dynamics, Bifurcations, and Control. Lecture Notes in Control and Information Sciences, vol 273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45606-6_13
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DOI: https://doi.org/10.1007/3-540-45606-6_13
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