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Asymptotic stability equals exponential stability, and ISS equals finite energy gain — if you twist your eyes |
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| Authors: | Lars Grüne Eduardo D Sontag Fabian R Wirth |
| Affiliation: | a Fachbereich Mathematik, J.W. Goethe-Universität, Postfach 11 19 32, D-60054 Frankfurt am Main, Germany;b Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA;c Zentrum für Technomathematik, Universität Bremen, D-28344 Bremen, Germany |
| Abstract: | In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H∞ estimate. |
| Keywords: | Asymptotic stability Exponential stability Input-to-state stability Nonlinear H∞ |
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