A numerical algorithm for solving the absolute stability problem in ℝ3

Michael Margaliot, Christos Yfoulis

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

Abstract

The problem of absolute stability is one of the oldest open problems in the theory of control. For low-order systems, the most general results were obtained by Pyatnitskiy and Rapoport. They derived an implicit characterization of the "most destabilizing" nonlinearity using the maximum principle. In this paper, we show that their approach yields a simple and efficient numerical scheme for solving the problem in the case of third-order systems. This allows the determination of the critical value where stability is lost in a tractable and accurate fashion. This value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem.

Original languageEnglish
Title of host publicationProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages7009-7013
Number of pages5
DOIs
StatePublished - 2005
Event44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain
Duration: 12 Dec 200515 Dec 2005

Publication series

NameProceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume2005

Conference

Conference44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/TerritorySpain
CitySeville
Period12/12/0515/12/05

Keywords

  • Differential inclusions
  • Global asymptotic stability under arbitrary switching
  • Switched controllers
  • Switched linear systems

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