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

✍ Scribed by Lars Grüne

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 264 KB
• Volume: 31
• Category: Article
• ISSN: 0936-7195
• DOI: 10.1002/gamm.200890005

✦ Synopsis

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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)