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

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dc.creatorGrüne, Lars
dc.creatorSontag, Eduardo D.
dc.creatorWirth, Fabian R.
dc.date1998-12-23
dc.date1999-05-19
dc.date.accessioned2026-07-07T05:27:21Z
dc.date.available2026-07-07T05:27:21Z
dc.descriptionIn 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.
dc.description14 pages, several references added, remarks section added, clarified construction
dc.identifierhttps://arxiv.org/abs/math/9812137
dc.identifierhttp://arxiv.org/abs/math/9812137
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77889
dc.subjectOptimization and Control
dc.subjectDynamical Systems
dc.subject34D05, 93D09
dc.titleAsymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes
dc.typetext

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