Stability Analysis Via Refinement of Piece-wise Linear Lyapunov Functions

Hasan A. Poonawala

doi:10.1109/CDC40024.2019.9030067

Stability Analysis Via Refinement of Piece-wise Linear Lyapunov Functions

Hasan A. Poonawala

Mechanical Engineering

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

3 Scopus citations

Abstract

We present an algorithm for finding piece-wise linear Lyapunov functions that verify the asymptotic stability of piece-wise linear differential inclusions. Existing methods either use a fixed set of pieces (a partition) to define the Lyapunov function, or use heuristic methods to split the pieces, thereby refining the partition. Our algorithm involves iteratively refining partitions using an exact criterion which strictly reduces the set of points over which the Lyapunov function is non-decreasing.

Original language	English
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Pages	1442-1447
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9030067
State	Published - Dec 2019
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: Dec 11 2019 → Dec 13 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	12/11/19 → 12/13/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC40024.2019.9030067

Cite this

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title = "Stability Analysis Via Refinement of Piece-wise Linear Lyapunov Functions",

abstract = "We present an algorithm for finding piece-wise linear Lyapunov functions that verify the asymptotic stability of piece-wise linear differential inclusions. Existing methods either use a fixed set of pieces (a partition) to define the Lyapunov function, or use heuristic methods to split the pieces, thereby refining the partition. Our algorithm involves iteratively refining partitions using an exact criterion which strictly reduces the set of points over which the Lyapunov function is non-decreasing.",

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doi = "10.1109/CDC40024.2019.9030067",

language = "English",

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Poonawala, HA 2019, Stability Analysis Via Refinement of Piece-wise Linear Lyapunov Functions. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9030067, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, pp. 1442-1447, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 12/11/19. https://doi.org/10.1109/CDC40024.2019.9030067

Stability Analysis Via Refinement of Piece-wise Linear Lyapunov Functions. / Poonawala, Hasan A.

2019 IEEE 58th Conference on Decision and Control, CDC 2019. 2019. p. 1442-1447 9030067 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

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

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AB - We present an algorithm for finding piece-wise linear Lyapunov functions that verify the asymptotic stability of piece-wise linear differential inclusions. Existing methods either use a fixed set of pieces (a partition) to define the Lyapunov function, or use heuristic methods to split the pieces, thereby refining the partition. Our algorithm involves iteratively refining partitions using an exact criterion which strictly reduces the set of points over which the Lyapunov function is non-decreasing.

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Stability Analysis Via Refinement of Piece-wise Linear Lyapunov Functions

Abstract

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