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Computing Upper-bounds of the Minimum Dwell Time of Linear Switched Systems via Homogeneous Polynomial Lyapunov Functions

Chesi, D. and Colaneri, P. and Geromel, J.C. and Middleton, R. and Shorten, R. (2010) Computing Upper-bounds of the Minimum Dwell Time of Linear Switched Systems via Homogeneous Polynomial Lyapunov Functions. American Control Conference (ACC), Proceedings, 2010. ISBN 978-1-4244-7426-4 . pp. 2487-2492. ISSN 0743-1619

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Abstract

This paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization problems based on linear matrix inequalities (LMIs). This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based on Kronecker products, and the other on the square matrix representation (SMR). Some examples illustrate the use and the potentialities of the proposed approach. It is also conjectured that the proposed approach is asymptotically nonconservative, i.e. the exact minimum dwell time is obtained by using homogeneous polynomials with sufficiently large degree.

Item Type: Article
Additional Information: ©2010 IEEE. 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; convex programming; linear matrix inequalities; polynomials; time-varying systems;
Subjects: Science & Engineering > Hamilton Institute
Item ID: 2243
Depositing User: Professor Rick Middleton
Date Deposited: 10 Nov 2010 16:34
Journal or Publication Title: American Control Conference (ACC), Proceedings, 2010. ISBN 978-1-4244-7426-4
Publisher: IEEE
Refereed: Yes
URI:

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