Invariance-Like Theorems and "lim inf" Convergence Properties

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 resem...

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Veröffentlicht in:	IEEE transactions on automatic control 2016-03, Vol.61 (3), p.648-661
Hauptverfasser:	Scarciotti, Giordano, Praly, Laurent, Astolfi, Alessandro
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic stability Automatic control Convergence Dynamical systems Electronic mail Invariance Linear matrix inequalities Lyapunov methods Nonlinear systems Theorems Trajectory
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Beschreibung
Zusammenfassung:	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.
ISSN:	0018-9286 1558-2523
DOI:	10.1109/TAC.2015.2444132