Constrained Nonlinear Polynomial Time-Delay Systems: A Sum-of-Squares Approach to Estimate the Domain of Attraction

Author

Franze, Giuseppe ; Famularo, Domenico ; Casavola, Alessandro

Author_Institution

DEIS, Univ. degli Studi della Calabria, Rende, Italy

Volume

57

Issue

10

fYear

2012

Firstpage

2673

Lastpage

2679

Abstract

A sum-of-squares (SOS) approach is proposed to estimate the domain of attraction (DoA) of regulated nonlinear polynomial time-delay systems subject to input constraints. It will be shown that the joint use of semialgebraic geometric arguments and semidefinite programming methods provides an efficient tool for Lyapunov-based control system analysis and design for this class of nonlinear delayed systems. Specifically, a two-step procedure is presented which consists of deriving first a Lyapunov-Krasovskii functional/controller pair complying with the prescribed constraints and computing then an estimate of the DoA.

Keywords

Lyapunov methods; algebra; control system analysis; delays; geometry; mathematical programming; nonlinear control systems; DoA; Lyapunov-Krasovskii functional; Lyapunov-based control system analysis; SOS; constrained nonlinear polynomial time-delay systems; domain of attraction; nonlinear delayed systems; semialgebraic geometric arguments; semidefinite programming methods; sum-of-squares approach; two-step procedure; Approximation methods; Asymptotic stability; Delay; Direction of arrival estimation; Optimization; Polynomials; Stability analysis; Domain of attraction (DoA); sum-of-squares (SOS);

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2012.2190189

Filename

6166434