Lars Grüne, Eduardo D Sontag, Fabian Wirth
Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes
The paper is published: Systems and Control Letters, 38(2):127-134, 1999
MSC:
93B52 Feedback control
93C55 Discrete-time
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.

Keywords: asymptotic stability, exponential stability, input-to-state stability, state transformation