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

L. Grüne, E. Sontag, F. Wirth: Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes
Systems & Control Letters 38, 127 - 134, 1999

Smart-Link: http://www.elsevier.com/locate/sysconle
DOI: 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 $H_\infty$ estimate.

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