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    On Common Quadratic Lyapunov Functions for Pairs of Stable LTI Systems Whose System Matrices Are in Companion Form

    Shorten, Robert N. and Narendra, Kumpati S. (2003) On Common Quadratic Lyapunov Functions for Pairs of Stable LTI Systems Whose System Matrices Are in Companion Form. IEEE Transactions on Automatic Control, 48 (4). pp. 618-621. ISSN 0018-9286

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    In this note, the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices A1 and A2 are in companion form is considered. It is shown that a necessary and sufficient condition for the existence of such a function is that the matrix product A1A2 does not have an eigenvalue that is real and negative. Examples are presented to illustrate the result.

    Item Type: Article
    Additional Information: "©2003 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: Lyapunov methods; Linear systems; Matrix algebra; Stability; Time-varying systems; Common quadratic Lyapunov functions; Necessary and sufficient conditions; Positive-definite real symmetric matrix; Quadratic stability; Stable LTI systems; Stable linear time-invariant systems; Switched linear systems; Hamilton Institute.
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 1856
    Identification Number:
    Depositing User: Hamilton Editor
    Date Deposited: 22 Feb 2010 17:25
    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

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