On a decomposition of multivariable forms via LMI methods

Author

Parrilo, Pablo A.

Author_Institution

Control & Dynamical Syst., California Inst. of Technol., Pasadena, CA, USA

Volume

1

Issue

6

fYear

2000

fDate

36770

Firstpage

322

Abstract

In this paper, it is shown that some of the convenient characteristics of LMI-based methods can be extended to a class of nonlinear systems. The main idea is to use a computationally tractable sufficient condition for positivity of a function, namely the existence of a “sum of squares” representation. By using an extended set of variables and redundant constraints, it is shown that the conditions can be written as linear matrix inequalities in the unknown parameters. To illustrate the method, we present an example dealing with the Lyapunov stability of systems described by polynomial vector fields

Keywords

Lyapunov methods; computational complexity; nonlinear systems; polynomial matrices; stability; Lyapunov stability; computational complexity; decomposition; linear matrix inequality; nonlinear systems; polynomial vector fields; positivity; sufficient condition; Control systems; Linear matrix inequalities; Lyapunov method; Nonlinear control systems; Nonlinear systems; Polynomials; Stability analysis; Sufficient conditions; Testing; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2000. Proceedings of the 2000

Conference_Location

Chicago, IL

ISSN

0743-1619

Print_ISBN

0-7803-5519-9

Type

conf

DOI

10.1109/ACC.2000.878894

Filename

878894