Estimation of asymptotic stability regions via composite homogeneous polynomial Lyapunov functions

In this article, we present a new method to estimate the asymptotic stability regions for a class of nonlinear systems via composite homogeneous polynomial Lyapunov functions, where these nonlinear systems are approximated as a convex hull of some linear systems. Since level set of the composite hom...

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Bibliographic Details
Published inInternational journal of control Vol. 88; no. 3; pp. 484 - 493
Main Authors Pang, Guochen, Zhang, Kanjian
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.03.2015
Taylor & Francis Ltd
Subjects
Asymptotic properties
asymptotic stability region
composite Lyapunov function
Dynamical systems
homogeneous polynomial function
invariant set
Lyapunov functions
Mathematical models
Nonlinear dynamics
Nonlinear programming
Nonlinear systems
Polynomials
Stability
Unions
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Summary:In this article, we present a new method to estimate the asymptotic stability regions for a class of nonlinear systems via composite homogeneous polynomial Lyapunov functions, where these nonlinear systems are approximated as a convex hull of some linear systems. Since level set of the composite homogeneous polynomial Lyapunov functions is a union set of several homogeneous polynomial functions, the composite homogeneous polynomial Lyapunov functions are nonconservative compared with quadratic or homogeneous polynomial Lyapunov functions. Numerical examples are used to illustrate the effectiveness of our method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2014.962616