Minimum achievable decay rates of the discrete linear inclusion

Ray Essick, Geir Dullerud

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

Abstract

In this paper we provide a scheme for estimating the minimum achievable exponential decay rate of a switched linear system via output feedback control. The output feedback stabilization of switched linear systems using path-dependent controllers is characterized exactly in [8] in terms of an increasing family of linear matrix inequalities; the feasibility of any one of these inequalities allows for the construction of a stabilizing controller, while infeasible conditions are disregarded. In this paper we use the infeasibility of these conditions to provide a lower bound on the achievable decay rate of the closed-loop system. We consider the special case of the discrete linear inclusion - e.g., a system with unrestricted switching - and develop a family of estimators of the minimum achievable decay rate for the system. For controllers of a fixed path-dependence, the resulting bounds provide an interval containing the minimum performance level whose length may be made as small as desired. The lower bound of these intervals is used as a nondecreasing estimation of the achievable decay rate. A simple, physically motivated example is provided to demonstrate the practical application of this result.

Original languageEnglish (US)
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1089-1094
Number of pages6
ISBN (Electronic)9781479986842
DOIs
StatePublished - Jul 28 2015
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

NameProceedings of the American Control Conference
Volume2015-July
ISSN (Print)0743-1619

Other

Other2015 American Control Conference, ACC 2015
CountryUnited States
CityChicago
Period7/1/157/3/15

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ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Essick, R., & Dullerud, G. (2015). Minimum achievable decay rates of the discrete linear inclusion. In ACC 2015 - 2015 American Control Conference (pp. 1089-1094). [7170878] (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7170878