Lyapunov Function Synthesis - Infeasibility and Farkas’ Lemma

Tobias Leth; Christoffer Sloth; Rafał Wisniewski; Sriram Sankaranarayanan

doi:10.1016/j.ifacol.2017.08.339

Lyapunov Function Synthesis - Infeasibility and Farkas’ Lemma

Tobias Leth, Christoffer Sloth, Rafał Wisniewski, Sriram Sankaranarayanan

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

Abstract

In this paper we prove the convergence of an algorithm synthesising continuous piecewise-polynomial Lyapunov functions for polynomial vector fields defined on simplices. We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems. We prove that this modification 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	2405-8971
DOIs	https://doi.org/10.1016/j.ifacol.2017.08.339
Publication status	Published - 2017
Externally published	Yes

Keywords

Algorithmic design
Lyapunov methods
Stability of nonlinear systems

Documents & Links

10.1016/j.ifacol.2017.08.339

Cite this

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title = "Lyapunov Function Synthesis - Infeasibility and Farkas{\textquoteright} Lemma",

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

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AU - Sloth, Christoffer

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AU - Sankaranarayanan, Sriram

PY - 2017

Y1 - 2017

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

KW - Algorithmic design

KW - Lyapunov methods

KW - Stability of nonlinear systems

U2 - 10.1016/j.ifacol.2017.08.339

DO - 10.1016/j.ifacol.2017.08.339

M3 - Journal article

AN - SCOPUS:85031790643

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VL - 50

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Lyapunov Function Synthesis - Infeasibility and Farkas’ Lemma

Abstract

Keywords

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