Almost global stability results for a class of singularly perturbed systems

Pietro Lorenzetti, George Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider a classical singularly perturbed system consisting of a slow subsystem with state x and a fast subsystem with state z, where the small parameter ε multiplies the derivative of z. We assume that the fast system is almost globally asymptotically stable (aGAS) for each fixed x, and the slow system, with z replaced by its equilibrium value, is globally asymptotically stable. We show that there exists a sufficiently small ε > 0 such that the equilibrium point of the overall system is aGAS for all ε ∈ (0, ε). We use the theory of density functions as developed by A. Rantzer, D. Angeli and R. Rajaram.

Original languageEnglish
Title of host publicationIFAC-PapersOnLine
EditorsHideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
PublisherElsevier B.V.
Pages809-814
Number of pages6
Edition2
ISBN (Electronic)9781713872344
DOIs
StatePublished - 1 Jul 2023
Event22nd IFAC World Congress - Yokohama, Japan
Duration: 9 Jul 202314 Jul 2023

Publication series

NameIFAC-PapersOnLine
Number2
Volume56
ISSN (Electronic)2405-8963

Conference

Conference22nd IFAC World Congress
Country/TerritoryJapan
CityYokohama
Period9/07/2314/07/23

Funding

FundersFunder number
Israel Science Foundation2802/21
Israel Science Foundation
Ministry of Energy, Israel219-11-128
Ministry of Energy, Israel

    Keywords

    • almost global stability
    • density functions
    • nonlinear systems
    • singular perturbations

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