A least-square spectral element method for stability analysis of time delay systems

David Lehotzky, T. Insperger

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents a numerical method for the stability analysis of retarded functional differential equations with time-periodic coefficients. The method approximates the solution segments, corresponding to the end points of the principal period, by their piecewise Lagrange interpolants. Then a mapping between these solution segments is obtained by the minimization of the least-square integral of the residual error. Finally stability properties are determined using the matrix approximation of the monodromy operator, obtained by this mapping, according to the Floquet theorem. The formulation of the method is presented for an equation of general type while results are shown for the delayed oscillator.

Original languageEnglish
Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
PublisherIFAC Secretariat
Pages382-385
Number of pages4
Volume48
Edition12
DOIs
Publication statusPublished - Jul 1 2015
Event12th IFAC Workshop on Time Delay Systems, TDS 2015 - Ann Arbor, United States
Duration: Jun 28 2015Jun 30 2015

Other

Other12th IFAC Workshop on Time Delay Systems, TDS 2015
CountryUnited States
CityAnn Arbor
Period6/28/156/30/15

Fingerprint

Time delay
Convergence of numerical methods
Numerical methods
Differential equations

Keywords

  • Least-squares method
  • Numerical method
  • Spectral element
  • Stability analysis
  • Stability domains
  • Time delay
  • Time-varying system

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Lehotzky, D., & Insperger, T. (2015). A least-square spectral element method for stability analysis of time delay systems. In IFAC Proceedings Volumes (IFAC-PapersOnline) (12 ed., Vol. 48, pp. 382-385). IFAC Secretariat. https://doi.org/10.1016/j.ifacol.2015.09.408

A least-square spectral element method for stability analysis of time delay systems. / Lehotzky, David; Insperger, T.

IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 48 12. ed. IFAC Secretariat, 2015. p. 382-385.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lehotzky, D & Insperger, T 2015, A least-square spectral element method for stability analysis of time delay systems. in IFAC Proceedings Volumes (IFAC-PapersOnline). 12 edn, vol. 48, IFAC Secretariat, pp. 382-385, 12th IFAC Workshop on Time Delay Systems, TDS 2015, Ann Arbor, United States, 6/28/15. https://doi.org/10.1016/j.ifacol.2015.09.408
Lehotzky D, Insperger T. A least-square spectral element method for stability analysis of time delay systems. In IFAC Proceedings Volumes (IFAC-PapersOnline). 12 ed. Vol. 48. IFAC Secretariat. 2015. p. 382-385 https://doi.org/10.1016/j.ifacol.2015.09.408
Lehotzky, David ; Insperger, T. / A least-square spectral element method for stability analysis of time delay systems. IFAC Proceedings Volumes (IFAC-PapersOnline). Vol. 48 12. ed. IFAC Secretariat, 2015. pp. 382-385
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