Common Quadratic Lyapunov Functions for Sets of Second-Order Linear Systems: A Simple Graphical Criterion

被引：0

作者：

Bainier, Gustave ^{[1
]}

Marx, Benoit ^{[1
]}

Ponsart, Jean-Christophe ^{[1
]}

机构：

[1] Univ Lorraine, CNRS, CRAN, F-54000 Nancy, France

来源：

IEEE CONTROL SYSTEMS LETTERS | 2024年 / 8卷

关键词：

Lyapunov methods; Asymptotic stability; Symmetric matrices; Stability criteria; Linear systems; Trajectory; Linear matrix inequalities; stability of nonlinear systems; stability of linear systems; SUFFICIENT CONDITIONS; EXISTENCE; STABILITY;

D O I：

10.1109/LCSYS.2024.3418672

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This letter presents a simple graphical criterion to obtain all common quadratic Lyapunov functions for nonlinear systems contained in the convex-hull of a set of second-order linear time-invariant systems. It simply consists in finding the intersection between the interior of some ellipses. The proposed criterion is declined for both continuous-time and discrete-time systems and is illustrated by numerical examples.

引用

页码：1889 / 1894

页数：6

共 20 条

[1] Conditions on the stability of a class of second-order switched systems [J].

Akar, M ;

Paul, A ;

Safonov, MG ;

Mitra, U .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (02) :338-340

[2]

[Anonymous], 1993, Nonlinear Systems Analysis

[3] Generalized nonlinear sector approaches for Takagi-Sugeno models [J].

Bainier, Gustave ;

Marx, Benoit ;

Ponsart, Jean-Christophe .

FUZZY SETS AND SYSTEMS, 2024, 476

[4]

Bof N, 2018, Arxiv, DOI arXiv:1809.05289

[5]

Boyd S., 1994, LINEAR MATRIX INEQUA

[6]

Boyd Stephen, 2004, Convex Optimization

[7]

Cannon J W, 1997, Math. Sci. Res. Inst. Publ., V31, P59

[8]

Jackson J. S, 1873, Geometrical Conic Sections: An Elementary Treatise in Which the Conic Sections are Defined as the Plane Sections of a Cone, and Treated by the Method of Projections

[9]

Khalil H.K., 2001, Nonlinear Systems, V3rd ed.

[10] On the existence of a common quadratic Lyapunov function for a rank one difference [J].

King, Christopher ;

Nathanson, Michael .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 419 (2-3) :400-416

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