DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005456
URN to cite this document: urn:nbn:de:bvb:703-epub-5456-9
URN to cite this document: urn:nbn:de:bvb:703-epub-5456-9
Title data
Grüne, Lars ; Sontag, Eduardo D. ; Wirth, Fabian:
Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes.
Bayreuth
,
1999
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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∞ estimate.