Quadratic Stability and Singular SISO Switching Systems

Shorten, Robert N. and Corless, Martin and Wulff, Kai and Middleton, Richard H. (2009) Quadratic Stability and Singular SISO Switching Systems. IEEE Transactions on Automatic Control, 54 (11). pp. 2714-2718. ISSN 0018-9286

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In this note, we consider 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 are of the form A, A-ghT, and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of the product A(A-ghT). The technical note also contains a spectral characterization of strictly positive real transfer functions which are strictly proper. Examples are presented to illustrate our results.

Item Type: Article
Additional Information: Copyright Notice "©2009 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=5288554&isnumber=5306469
Keywords: LTI systems; Linear time-invariant systems; Quadratic Stability; Singular SISO Switching Systems; Hamilton Institute.
Academic Unit: Faculty of Science and Engineering > Computer Science
Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID: 1639
Identification Number: 10.1109/TAC.2009.2031586
Depositing User: Hamilton Editor
Date Deposited: 04 Nov 2009 15:06
Journal or Publication Title: IEEE Transactions on Automatic Control
Publisher: IEEE
Refereed: Yes

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