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On the Stability of Switched Positive Linear Systems

Gurvits, L. and Shorten, R. and Mason, O. (2007) On the Stability of Switched Positive Linear Systems. IEEE Transactions on Automatic Control, 52 (6). pp. 1099-1103. ISSN 0018-9286

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Abstract

It was recently conjectured that the Hurwitz stability of the convex hull of a set of Metzler matrices is a necessary and sufficient condition for the asymptotic stability of the associated switched linear system under arbitrary switching. In this note, we show that 1) this conjecture is true for systems constructed from a pair of second-order Metzler matrices; 2) the conjecture is true for systems constructed from an arbitrary finite number of second-order Metzler matrices; and 3) the conjecture is in general false for higher order systems. The implications of our results, both for the design of switched positive linear systems, and for research directions that arise as a result of our work, are discussed toward the end of the note.

Item Type: Article
Additional Information: "©2007 IEEE. Reprinted from IEEE Transactions on Automatic Control. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4237306&isnumber=4237288
Keywords: Asymptotic stability; Linear systems; Matrix algebra; Time-varying systems; Hurwitz stability; Metzler matrices; Arbitrary switching; Higher order systems; Switched positive linear systems; Positive linear systems; Stability theory; Switched linear systems; Hamilton Institute.
Subjects: Science & Engineering > Hamilton Institute
Science & Engineering > Computer Science
Item ID: 1717
Identification Number: 10.1109/TAC.2007.899057
Depositing User: Hamilton Editor
Date Deposited: 02 Dec 2009 16:17
Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Refereed: Yes
URI:

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