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Invariance-like theorems and weak convergence properties

Abstract : Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “lim inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “lim inf” Matrosov and Small-gain theorems and are based on a “lim inf” Barbalat's Lemma. Additional technical assumptions to have “lim” convergence are given: the “lim inf”/“lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples.
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Submitted on : Tuesday, January 24, 2017 - 12:21:56 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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Giordano Scarciotti, Laurent Praly, Alessandro Astolfi. Invariance-like theorems and weak convergence properties. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2016, 61 (3), pp.648 - 661. ⟨10.1109/TAC.2015.2444132⟩. ⟨hal-01444785⟩

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