Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems

Matthew Abate; Corbin Klett; Samuel Coogan; Eric Feron

doi:10.23919/ACC45564.2020.9147662

Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems

Matthew Abate, Corbin Klett, Samuel Coogan, Eric Feron

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

5 Scopus citations

Abstract

This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic Lyapunov functions for a related hierarchy of Lyapunov differential equations. This creates an intuitive procedure for checking the stability properties of switched linear systems, and a computationally competitive algorithm is presented for generating high-order homogeneous polynomial Lyapunov functions in this manner. Additionally, we provide a comparison between polynomial Lyapunov functions generated with our proposed approach and Lyapunov functions generated with a more traditional sum-of-squares based approach.

Original language	English (US)
Title of host publication	Proceedings of the American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5322-5327
Number of pages	6
ISBN (Print)	9781538682661
DOIs	https://doi.org/10.23919/ACC45564.2020.9147662
State	Published - Jul 1 2020
Externally published	Yes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2021-02-18

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10.23919/ACC45564.2020.9147662

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title = "Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems",

abstract = "This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic Lyapunov functions for a related hierarchy of Lyapunov differential equations. This creates an intuitive procedure for checking the stability properties of switched linear systems, and a computationally competitive algorithm is presented for generating high-order homogeneous polynomial Lyapunov functions in this manner. Additionally, we provide a comparison between polynomial Lyapunov functions generated with our proposed approach and Lyapunov functions generated with a more traditional sum-of-squares based approach.",

author = "Matthew Abate and Corbin Klett and Samuel Coogan and Eric Feron",

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doi = "10.23919/ACC45564.2020.9147662",

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Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems. / Abate, Matthew; Klett, Corbin; Coogan, Samuel et al.
Proceedings of the American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2020. p. 5322-5327.

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

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T1 - Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems

AU - Abate, Matthew

AU - Klett, Corbin

AU - Coogan, Samuel

AU - Feron, Eric

N1 - Generated from Scopus record by KAUST IRTS on 2021-02-18

PY - 2020/7/1

Y1 - 2020/7/1

N2 - This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic Lyapunov functions for a related hierarchy of Lyapunov differential equations. This creates an intuitive procedure for checking the stability properties of switched linear systems, and a computationally competitive algorithm is presented for generating high-order homogeneous polynomial Lyapunov functions in this manner. Additionally, we provide a comparison between polynomial Lyapunov functions generated with our proposed approach and Lyapunov functions generated with a more traditional sum-of-squares based approach.

AB - This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic Lyapunov functions for a related hierarchy of Lyapunov differential equations. This creates an intuitive procedure for checking the stability properties of switched linear systems, and a computationally competitive algorithm is presented for generating high-order homogeneous polynomial Lyapunov functions in this manner. Additionally, we provide a comparison between polynomial Lyapunov functions generated with our proposed approach and Lyapunov functions generated with a more traditional sum-of-squares based approach.

UR - https://ieeexplore.ieee.org/document/9147662/

UR - http://www.scopus.com/inward/record.url?scp=85089597707&partnerID=8YFLogxK

U2 - 10.23919/ACC45564.2020.9147662

DO - 10.23919/ACC45564.2020.9147662

M3 - Conference contribution

SN - 9781538682661

SP - 5322

EP - 5327

BT - Proceedings of the American Control Conference

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems

Abstract

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