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

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

1998-12-23

arxiv.org/abs/math/9812137v3

Mathematics

Optimization and Control

14 pages, several references added, remarks section added, clarified construction

Scientific paper

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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