On infinity norms as Lyapunov functions for piecewise affine systems

M. Lazar; A. Jokic

doi:10.1145/1755952.1755972

On infinity norms as Lyapunov functions for piecewise affine systems

M. Lazar, A. Jokic

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

14 Citations (Scopus)

201 Downloads (Pure)

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 language	English
Title of host publication	Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control (HSCC), 12-16 April 2010, Stockholm, Sweden
Place of Publication	Berlin
Publisher	Springer
Pages	131-140
ISBN (Print)	978-1-60558-955-8
DOIs	https://doi.org/10.1145/1755952.1755972
Publication status	Published - 2010

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title = "On infinity norms as Lyapunov functions for piecewise affine systems",

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.",

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On infinity norms as Lyapunov functions for piecewise affine systems. / Lazar, M.; Jokic, A.

Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control (HSCC), 12-16 April 2010, Stockholm, Sweden. Berlin : Springer, 2010. p. 131-140.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Jokic, A.

PY - 2010

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N2 - 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.

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M3 - Conference contribution

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BT - Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control (HSCC), 12-16 April 2010, Stockholm, Sweden

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On infinity norms as Lyapunov functions for piecewise affine systems

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