MURAL - Maynooth University Research Archive Library

    On the Stability of Switched Positive Linear Systems

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

    [img] Download (214kB)
    Official URL:

    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...

    Add this article to your Mendeley library


    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."
    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.
    Academic Unit: Faculty of Science and Engineering > Computer Science
    Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 1717
    Identification Number:
    Depositing User: Hamilton Editor
    Date Deposited: 02 Dec 2009 16:17
    Journal or Publication Title: IEEE Transactions on Automatic Control
    Publisher: IEEE
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

    Repository Staff Only(login required)

    View Item Item control page


    Downloads per month over past year

    Origin of downloads