Lyapunov Function Synthesis - Infeasibility and Farkas' Lemma

Tobias Leth; Christoffer Sloth; Rafal Wisniewski; Sriram Sankaranarayanan

doi:10.1016/j.ifacol.2017.08.339

Lyapunov Function Synthesis - Infeasibility and Farkas' Lemma

Tobias Leth, Christoffer Sloth, Rafal Wisniewski, Sriram Sankaranarayanan

Research output: Contribution to journal › Conference article in Journal › Research › peer-review

3 Citations (Scopus)

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Abstract

In this paper we prove the convergence of an algorithm synthesising continuous piecewise-polynomial Lyapunov functions for polynomial vector elds dened on simplices. We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems. We prove that this modication does not destroy the convergence of the algorithm. Both methods are accompanied by examples.

Original language	English
Book series	IFAC-PapersOnLine
Volume	50
Issue number	1
Pages (from-to)	1667-1672
ISSN	2405-8963
DOIs	https://doi.org/10.1016/j.ifacol.2017.08.339
Publication status	Published - 10 Jul 2017
Event	2017 IFAC Congress - Duration: 9 Jul 2017 → 14 Jul 2017 https://www.ifac2017.org/

Conference

Conference	2017 IFAC Congress
Period	09/07/2017 → 14/07/2017
Internet address	https://www.ifac2017.org/

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10.1016/j.ifacol.2017.08.339

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Cite this

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title = "Lyapunov Function Synthesis - Infeasibility and Farkas' Lemma",

abstract = "In this paper we prove the convergence of an algorithm synthesising continuous piecewise-polynomial Lyapunov functions for polynomial vector elds dened on simplices. We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems. We prove that this modication does not destroy the convergence of the algorithm. Both methods are accompanied by examples.",

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AU - Sankaranarayanan, Sriram

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N2 - In this paper we prove the convergence of an algorithm synthesising continuous piecewise-polynomial Lyapunov functions for polynomial vector elds dened on simplices. We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems. We prove that this modication does not destroy the convergence of the algorithm. Both methods are accompanied by examples.

AB - In this paper we prove the convergence of an algorithm synthesising continuous piecewise-polynomial Lyapunov functions for polynomial vector elds dened on simplices. We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems. We prove that this modication does not destroy the convergence of the algorithm. Both methods are accompanied by examples.

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DO - 10.1016/j.ifacol.2017.08.339

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