Invariance-like theorems and “lim inf” convergence properties
File(s)Paper_4.pdf (2.71 MB)
Accepted version
Author(s)
Scarciotti, G
Praly, L
Astolfi, A
Type
Journal Article
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.
Date Issued
2015-06-11
Date Acceptance
2015-06-01
Citation
IEEE Transactions on Automatic Control, 2015, 61 (3), pp.648-661
ISSN
1558-2523
Publisher
IEEE
Start Page
648
End Page
661
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
61
Issue
3
Copyright Statement
© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Subjects
Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Krasovskii-LaSalle invariance
Lyapunov theorems
Matrosov theorem
SMALL-GAIN THEOREM
ISS SYSTEMS
LYAPUNOV FUNCTIONS
INTERCONNECTED IISS
MATROSOV THEOREM
STABILITY
Industrial Engineering & Automation
0906 Electrical And Electronic Engineering
0102 Applied Mathematics
0913 Mechanical Engineering
Publication Status
Published