Convergence Rates of Perturbed Attracting Sets with Vanishing Perturbations

L. Grüne: Convergence Rates of Perturbed Attracting Sets with Vanishing Perturbations
Journal of Mathematical Analysis and Applications 244, 369 - 392, 2000

DOI: 10.1006/jmaa.2000.6707
Keywords: time varying perturbations; convergence; exponentially attracting sets
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Abstract:

We investigate the rate of convergence and the rate of attraction of perturbed attracting sets as the perturbation tends to zero. The perturbation model under consideration is a control system which contains the unperturbed system as zero dynamics. Necessary and sufficient conditions for certain rates of convergence are derived. Several applications especially to numerical approximations are given and a number of examples illustrates the results.

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