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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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Abstract

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." http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1193741
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.
Subjects: Science & Engineering > Electronic Engineering
Science & Engineering > Hamilton Institute
Science & Engineering > Mathematics & Statistics
Item ID: 1856
Identification Number: 10.1109/TAC.2003.809795
Depositing User: Hamilton Editor
Date Deposited: 22 Feb 2010 17:25
Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Refereed: Yes
URI:

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