Analysis of Polynomial Systems With Time Delays via the Sum of Squares Decomposition

Author

Papachristodoulou, Antonis ; Peet, Matthew M. ; Lall, Sanjay

Author_Institution

Dept. of Eng. Sci., Univ. of Oxford, Oxford

Volume

54

Issue

5

fYear

2009

fDate

5/1/2009 12:00:00 AM

Firstpage

1058

Lastpage

1064

Abstract

We present a methodology for analyzing robust independent-of-delay and delay-dependent stability of equilibria of systems described by nonlinear Delay Differential Equations by algorithmically constructing appropriate Lyapunov-Krasovskii functionals using the sum of squares decomposition of multivariate polynomials and semidefinite programming. We illustrate the methodology using an example from population dynamics.

Keywords

Lyapunov methods; delay-differential systems; delays; nonlinear differential equations; polynomials; stability; Lyapunov-Krasovskii functionals; delay-dependent stability; independent-of-delay; multivariate polynomials; nonlinear delay differential equations; polynomial systems; semidefinite programming; sum of squares decomposition; time delays; Algorithm design and analysis; Delay effects; Differential equations; Functional programming; Linear matrix inequalities; Lyapunov method; Polynomials; Robust stability; Stability analysis; Testing; Linear matrix inequality (LMI); Lyapunov-Krasovskii; sum of squares (SOS); time delay;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2017168

Filename

4908924