Stability analysis of positive linear switched systems: A variational approach

Michael Margaliot*, Michael S. Branicky

*Corresponding author for this work

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

Abstract

We consider the stability analysis of switched systems under arbitrary switching laws. A powerful approach for addressing this problem is based on studying the "most unstable" switching law (MUSL). If the switched system is stable for the MUSL, it is stable for any switching law. The MUSL can be defined as the solution to a certain optimal control problem. The main analysis tool is then the celebrated maximum principle (MP). This provides an implicit characterization of the MUSL in terms of the adjoint and switching function defined in the MP. In this paper, we consider the optimal control problem defining the MUSL for the particular case of positive linear switched systems. We show that in this case the MP can be strengthened. Specifically, there exist regions in the state-space for which the MUSL is known explicitly.

Original languageEnglish
Title of host publicationROCOND'09 - 6th IFAC Symposium on Robust Control Design, Proceedings
Pages31-35
Number of pages5
EditionPART 1
DOIs
StatePublished - 2009
Event6th IFAC Symposium on Robust Control Design, ROCOND'09 - Haifa, Israel
Duration: 16 Jun 200918 Jun 2009

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
Volume6
ISSN (Print)1474-6670

Conference

Conference6th IFAC Symposium on Robust Control Design, ROCOND'09
Country/TerritoryIsrael
CityHaifa
Period16/06/0918/06/09

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