MINES ParisTech CAS - Centre automatique et systèmes

Invariance-like theorems and weak convergence properties

Authors: G. Scarciotti, L. Praly, A. Astolfi, IEEE Transactions on Automatic Control, Vol. 61 No 3, pp. 648 - 661, 11 June 2015, DOI: 10.1109/TAC.2015.2444132
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.
Download PDF
author = {L. Praly G. Scarciotti, A. Astolfi},
title = {Invariance-like theorems and weak convergence properties},
journal = {IEEE Transactions on Automatic Control},
volume = {61},
number = {3},
pages = {648 - 661},
year = {2015},