Stability of singularly perturbed functional-differential systems: Spectrum analysis and LMI approaches

Valery Y. Glizer*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A singularly perturbed linear functional-differential system is considered. The delay is assumed to be small of the order of a small parameter multiplying a part of derivatives in the system. It is 'not assumed that the fast subsystem is asymptotically stable'. Two approaches to the study of the exponential stability of the singularly perturbed system are suggested. The first one treats systems with constant delays via the analysis of asymptotic behaviour of the roots of their characteristic equation. The second approach develops a direct Lyapunov-Krasovskii method for systems with time-varying delays leading to stability conditions in terms of linear matrix inequalities. Numerical examples illustrate the efficiency of both approaches.

Original languageEnglish
Pages (from-to)79-111
Number of pages33
JournalIMA Journal of Mathematical Control and Information
Volume29
Issue number1
DOIs
StatePublished - Mar 2012

Funding

FundersFunder number
Kamea Fund of Israel
Israel Science Foundation754/10

    Keywords

    • exponential stability
    • functional-differential system
    • linear matrix inequality
    • singular perturbation
    • spectrum analysis

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