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

L. Grüne, E. Sontag, F. Wirth: 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, Phoenix, Arizona, 1999, 1220 - 1225

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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.

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