The minimum achievable stability radius of switched linear systems with feedback

Ray Essick, Matthew Philippe, Geir Dullerud, Raphael M. Jungers

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

Abstract

We present a scheme for estimating the minimum achievable decay rate of a switched linear system via path-dependent feedback control, when the switching signal belongs to a language generated by a strongly connected graph. This growth rate is characterized by the constrained joint spectral radius (CJSR) of the system, a generalization of the joint spectral radius to account for the switching constraint. Our key tool in analyizing the CJSR is the multinorm, a collection of mode-indexed norms which demonstrate contractiveness along admissible modal trajectories. We may approximate the CJSR to any desired accuracy by computing quadratic multinorms as solutions to a system of LMIs, using an estimation scheme presented in [15]. These LMIs are of similar form to those which characterize the stability of the switched system in [6]. The feasiblity of any one of these LMIs allows the construction of a suitable controller; we use the infeasibility of such an LMI to provide a lower bound on the closed-loop decay rate achieved by any path-dependent controller.

Original languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4240-4245
Number of pages6
ISBN (Electronic)9781479978861
DOIs
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
Country/TerritoryJapan
CityOsaka
Period12/15/1512/18/15

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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