Input-to-state stability, numerical dynamics and sampled-data control

L. Grüne: Input-to-state stability, numerical dynamics and sampled-data control
GAMM-Mitteilungen 31, 94 - 114, 2008

DOI: 10.1002/gamm.200890005
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Abstract:

We investigate the relation between asymptotic stability for dynamical systems and families of approximations. Using suitably perturbed systems and the input-to-state stability property we develop a framework which yields necessary and sufficient conditions on the stability of the approximations ensuring stability of the approximated system. The results are formulated for numerical one step schemes for ordinary differential equations and for sampled-data systems.

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