Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes

Titelangaben

Grüne, Lars ; Sontag, Eduardo D. ; Wirth, Fabian:
Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes.
Bayreuth , 1999

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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.