On infinity norms as Lyapunov functions for piecewise affine systems

M. Lazar, A. Jokic

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14 Citations (Scopus)
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Abstract

This paper considers off-line synthesis of stabilizing static feedback control laws for discrete-time piecewise affine (PWA) systems. Two of the problems of interest within this framework are: (i) incorporation of the S-procedure in synthesis of a stabilizing state feedback control law and (ii) synthesis of a stabilizing output feedback control law. Tackling these problems via (piecewise) quadratic Lyapunov function candidates yields a bilinear matrix inequality at best. A new solution to these problems is proposed in this work, which uses infinity norms as Lyapunov function candidates and, under certain conditions, requires solving a single linear program. This solution also facilitates the computation of piecewise polyhedral positively invariant (or contractive) sets for discrete-time PWA systems.
Original languageEnglish
Title of host publicationProceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control (HSCC), 12-16 April 2010, Stockholm, Sweden
Place of PublicationBerlin
PublisherSpringer
Pages131-140
ISBN (Print)978-1-60558-955-8
DOIs
Publication statusPublished - 2010

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