Common Lyapunov function computation for discrete-time systems

Sigurdur Freyr Hafstein

doi:10.1109/CDC.2018.8619234

Common Lyapunov function computation for discrete-time systems

Sigurdur Freyr Hafstein

Raunvísindadeild

Háskóli Íslands

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Útdráttur

We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.

Upprunalegt tungumál	Enska
Titill gistiútgáfu	2018 IEEE Conference on Decision and Control, CDC 2018
Útgefandi	Institute of Electrical and Electronics Engineers Inc.
Síður	3211-3216
Síðufjöldi	6
ISBN-númer (rafrænt)	9781538613955
DOI	https://doi.org/10.1109/CDC.2018.8619234
Útgáfustaða	Útgefið - 18 jan. 2019
Viðburður	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, Bandaríkin Tímalengd: 17 des. 2018 → 19 des. 2018

Ritröð

Nafn	Proceedings of the IEEE Conference on Decision and Control
Bindi	2018-December

Ráðstefna

Ráðstefna	57th IEEE Conference on Decision and Control, CDC 2018
Land/Yfirráðasvæði	Bandaríkin
Borg/bær	Miami
Tímabil	17/12/18 → 19/12/18

Athugasemd

Funding Information: This work was supported by the Icelandic Research Fund (Rannís) in the projects Lyapunov Methods and Stochastic Stability (nr. 152429-051) and Complete Lyapunov functions: Efficient numerical computation (nr. 163074-052). Publisher Copyright: © 2018 IEEE.

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10.1109/CDC.2018.8619234

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@inproceedings{562439bb2624431e927b2281fdd116b9,

title = "Common Lyapunov function computation for discrete-time systems",

abstract = "We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.",

author = "Hafstein, \{Sigurdur Freyr\}",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

year = "2019",

month = jan,

day = "18",

doi = "10.1109/CDC.2018.8619234",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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}

Hafstein, SF 2019, Common Lyapunov function computation for discrete-time systems. í 2018 IEEE Conference on Decision and Control, CDC 2018., 8619234, Proceedings of the IEEE Conference on Decision and Control, bind. 2018-December, Institute of Electrical and Electronics Engineers Inc., bls. 3211-3216, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, Bandaríkin, 17/12/18. https://doi.org/10.1109/CDC.2018.8619234

Common Lyapunov function computation for discrete-time systems. / Hafstein, Sigurdur Freyr.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. s. 3211-3216 8619234 (Proceedings of the IEEE Conference on Decision and Control; Bindi 2018-December).

Rannsóknarafurð: Kafli í bók/skýrslu/ráðstefnuriti › Ráðstefnuframlag › ritrýni

TY - GEN

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AU - Hafstein, Sigurdur Freyr

PY - 2019/1/18

Y1 - 2019/1/18

N2 - We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.

AB - We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.

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U2 - 10.1109/CDC.2018.8619234

DO - 10.1109/CDC.2018.8619234

M3 - Conference contribution

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3211

EP - 3216

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

Y2 - 17 December 2018 through 19 December 2018

ER -

Common Lyapunov function computation for discrete-time systems

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