Closed-Form Estimates of the Domain of Attraction for Nonlinear Systems via Fuzzy-Polynomial Models

Author

Pitarch, Jose Luis ; Sala, Alessandra ; Arino, Carlos V.

Author_Institution

Syst. Eng. & Control Dept., Univ. Politec. de Valencia, Valencia, Spain

Volume

44

Issue

4

fYear

2014

fDate

41730

Firstpage

526

Lastpage

538

Abstract

In this paper, the domain of attraction of the origin of a nonlinear system is estimated in closed form via level sets with polynomial boundaries, iteratively computed. In particular, the domain of attraction is expanded from a previous estimate, such as a classical Lyapunov level set. With the use of fuzzy-polynomial models, the domain of attraction analysis can be carried out via sum of squares optimization and an iterative algorithm. The result is a function that bounds the domain of attraction, free from the usual restriction of being positive and decrescent in all the interior of its level sets.

Keywords

Lyapunov methods; fuzzy set theory; iterative methods; nonlinear systems; optimisation; polynomials; classical Lyapunov level set; domain of attraction analysis; domain of attraction closed-form estimate; fuzzy-polynomial models; iterative algorithm; iterative computation; nonlinear systems; polynomial boundaries; sum of squares optimization; Domain of attraction; fuzzy polynomial systems; local stability; nonlinear systems; robust stability; sum of squares;

fLanguage

English

Journal_Title

Cybernetics, IEEE Transactions on

Publisher

ieee

ISSN

2168-2267

Type

jour

DOI

10.1109/TCYB.2013.2258910

Filename

6527923