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.
In: Systems & Control Letters. Bd. 38 (1999) Heft 2 . - S. 127-134.
ISSN 1872-7956
DOI: https://doi.org/10.1016/S0167-6911(99)00053-5

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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.