On the equivalence between asymptotic and exponential stability, and between ISS and finite H-infinity gain

Titelangaben

Grüne, Lars ; Sontag, Eduardo D. ; Wirth, Fabian:
On the equivalence between asymptotic and exponential stability, and between ISS and finite H-infinity gain.
In: Proceedings of the 38th IEEE Conference on Decision and Control. Volume 2. - Piscataway, NJ : IEEE , 1999 . - S. 1220-1225
ISBN 0-7803-5250-5

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Abstract

We show that uniformly global asymptotic stability and input-to-state stability for a family of ordinary differential equations are equivalent to uniformly global exponential stability and a nonlinear H-infinity estimate, respectively, under suitable nonlinear changes of variables.