Smallest Lyapunov Functions of Differential Inclusions

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/3168 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/3168 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/3168 archive 351 disk0/00/00/31/24 2016-01-15 01:58:49 2021-08-27 17:13:15 2016-01-15 01:58:49 monograph show 2 Aubin J.-P. 7347 Smallest Lyapunov Functions of Differential Inclusions pub iis_met prog_sds This paper provides a first answer to the question: does there exist a smallest Lyapunov function of a differential inclusion larger than a given function. For that purpose, they have to be looked for in the class of lower semicontinuous functions, and thus, the concept of derivative has to be replaced by the one of contingent epi-derivative to characterize lower semicontinuous Lyapunov functions. The existence of a largest closed viability (and/or invariance) domain of a differential inclusion contained in a given closed subset is then proved and used to infer the existence of such a Lyapunov function. 1988-09 published WP-88-081 WP-88-081 10 1134 public working_paper IIASA, Laxenburg, Austria 29 FALSE info:eu-repo/semantics/book