A Relaxation Theorem for Differential Inclusions with Applications to Stability Properties

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dc.creatorIngalls, Brian P.
dc.creatorSontag, Eduardo D.
dc.creatorWang, Yuan
dc.date2002-06-24
dc.date.accessioned2026-07-07T04:49:20Z
dc.date.available2026-07-07T04:49:20Z
dc.descriptionThe fundamental Filippov-Wazwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. In our recent work, a complementary result was provided for inclusions with finite dimensional state spaces which says that the approximation can be carried out over non-compact or infinite intervals provided one does not insist on the same initial values. This note extends the infinite-time relaxation theorem to the inclusions whose state spaces are Banach spaces. To illustrate the motivations for studying such approximation results, we briefly discuss a quick application of the result to output stability and uniform output stability properties.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0206251
dc.identifierhttp://arxiv.org/abs/math/0206251
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64381
dc.subjectDynamical Systems
dc.subjectOptimization and Control
dc.subject34A60
dc.titleA Relaxation Theorem for Differential Inclusions with Applications to Stability Properties
dc.typetext

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