Lars Grüne, Eduardo D Sontag, Fabian Wirth
Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes
The paper is published: Systems and Control Letters, 38(2):127-134, 1999
MSC:
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 $H_\infty$ estimate.


Keywords: asymptotic stability, exponential stability, input-to-state stability, state transformation

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Zentrum für Technomathematik (German)
Institute for Dynamical Systems
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The University of Bremen