Stability by averaging via time-varying Lyapunov functions

Rami Katz, Frédéric Mazenc*, Emilia Fridman

*Corresponding author for this work

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

Abstract

We study linear continuous-time systems with fast-varying almost periodic coefficients that are piecewise-continuous in time. Recently, a constructive time-delay approach to periodic averaging of systems with a single fast time-scale was introduced and employed to averaging of systems with small time-varying delays (of the order of the small parameter). In this paper we present a novel transformation of the fast varying coefficients. This transformation is suitable for averaging over multiple time-scales, and is applicable to averaging of systems with constant delays, where the value of delay is not small (i.e. essentially larger than the small parameter). We carry out stability analysis by employing time-varying Lyapunov functions (or functionals for the delayed case). The analysis leads to LMI conditions that are always feasible for small enough parameters. Numerical examples demonstrate the efficiency of the proposed approach and its conservatism.

Original languageEnglish
Title of host publicationIFAC-PapersOnLine
EditorsHideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
PublisherElsevier B.V.
Pages197-202
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

Keywords

  • averaging
  • stability
  • time-varying

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