Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems

Morgan Jones; Matthew M. Peet

doi:10.23919/ACC55779.2023.10155996

Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems

Morgan Jones, Matthew M. Peet

Engineering, Ira A. Fulton Schools of (IAFSE)

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

Abstract

This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The proposed method is particularly well suited to the stability analysis of ODEs with high dimensional state spaces. This is due to the fact that partially quadratic LFs are parametrized by fewer decision variables when compared with general SOS LFs. The main contribution of this paper is using the Center Manifold Theorem to show that partially quadratic LFs that certify the local asymptotic stability of a given ODE exist under certain conditions.

Original language	English (US)
Title of host publication	2023 American Control Conference, ACC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4130-4135
Number of pages	6
ISBN (Electronic)	9798350328066
DOIs	https://doi.org/10.23919/ACC55779.2023.10155996
State	Published - 2023
Event	2023 American Control Conference, ACC 2023 - San Diego, United States Duration: May 31 2023 → Jun 2 2023

Publication series

Name	Proceedings of the American Control Conference
Volume	2023-May
ISSN (Print)	0743-1619

Conference

Conference	2023 American Control Conference, ACC 2023
Country/Territory	United States
City	San Diego
Period	5/31/23 → 6/2/23

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.23919/ACC55779.2023.10155996

Cite this

Jones, M., & Peet, M. M. (2023). Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems. In 2023 American Control Conference, ACC 2023 (pp. 4130-4135). (Proceedings of the American Control Conference; Vol. 2023-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC55779.2023.10155996

Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems. / Jones, Morgan; Peet, Matthew M.
2023 American Control Conference, ACC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 4130-4135 (Proceedings of the American Control Conference; Vol. 2023-May).

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

Jones, M & Peet, MM 2023, Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems. in 2023 American Control Conference, ACC 2023. Proceedings of the American Control Conference, vol. 2023-May, Institute of Electrical and Electronics Engineers Inc., pp. 4130-4135, 2023 American Control Conference, ACC 2023, San Diego, United States, 5/31/23. https://doi.org/10.23919/ACC55779.2023.10155996

@inproceedings{a961e4967b144dcea8437292fa3ad136,

title = "Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems",

abstract = "This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The proposed method is particularly well suited to the stability analysis of ODEs with high dimensional state spaces. This is due to the fact that partially quadratic LFs are parametrized by fewer decision variables when compared with general SOS LFs. The main contribution of this paper is using the Center Manifold Theorem to show that partially quadratic LFs that certify the local asymptotic stability of a given ODE exist under certain conditions.",

author = "Morgan Jones and Peet, {Matthew M.}",

note = "Publisher Copyright: {\textcopyright} 2023 American Automatic Control Council.; 2023 American Control Conference, ACC 2023 ; Conference date: 31-05-2023 Through 02-06-2023",

year = "2023",

doi = "10.23919/ACC55779.2023.10155996",

language = "English (US)",

series = "Proceedings of the American Control Conference",

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

pages = "4130--4135",

booktitle = "2023 American Control Conference, ACC 2023",

}

TY - GEN

T1 - Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems

AU - Jones, Morgan

AU - Peet, Matthew M.

PY - 2023

Y1 - 2023

N2 - This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The proposed method is particularly well suited to the stability analysis of ODEs with high dimensional state spaces. This is due to the fact that partially quadratic LFs are parametrized by fewer decision variables when compared with general SOS LFs. The main contribution of this paper is using the Center Manifold Theorem to show that partially quadratic LFs that certify the local asymptotic stability of a given ODE exist under certain conditions.

AB - This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The proposed method is particularly well suited to the stability analysis of ODEs with high dimensional state spaces. This is due to the fact that partially quadratic LFs are parametrized by fewer decision variables when compared with general SOS LFs. The main contribution of this paper is using the Center Manifold Theorem to show that partially quadratic LFs that certify the local asymptotic stability of a given ODE exist under certain conditions.

UR - http://www.scopus.com/inward/record.url?scp=85167829935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85167829935&partnerID=8YFLogxK

U2 - 10.23919/ACC55779.2023.10155996

DO - 10.23919/ACC55779.2023.10155996

M3 - Conference contribution

AN - SCOPUS:85167829935

T3 - Proceedings of the American Control Conference

SP - 4130

EP - 4135

BT - 2023 American Control Conference, ACC 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2023 American Control Conference, ACC 2023

Y2 - 31 May 2023 through 2 June 2023

ER -

Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this