Stability Analysis of Time-Delay Systems With Incommensurate Delays Using Positive Polynomials

Author

Münz, Ulrich ; Ebenbauer, Christian ; Haag, Thomas ; Allgöwer, Frank

Author_Institution

Inst. for Syst. Theor. & Autom. Control, Univ. of Stuttgart, Stuttgart

Volume

54

Issue

5

fYear

2009

fDate

5/1/2009 12:00:00 AM

Firstpage

1019

Lastpage

1024

Abstract

We present a new stability condition for linear time-delay systems (TDS) with multiple incommensurate delays based on the Rekasius substitution and positive polynomials. The condition is checked by testing the positivity of multivariate polynomials in certain domains. For this purpose, we propose two alternative algorithms based on linear programming and sum of squares methods, respectively. The efficiency and accuracy of the algorithms is compared in an example to alternative stability conditions taken from the literature.

Keywords

delay systems; delays; linear programming; polynomials; stability; incommensurate delays; linear programming; linear time-delay systems; multivariate polynomials; positive polynomials; stability analysis; sum of squares methods; Asymptotic stability; Automatic control; Delay lines; Delay systems; Frequency domain analysis; Linear programming; Polynomials; Stability analysis; State-space methods; Testing; Incommensurate delays; Rekasius substitution; linear programming; sum of squares; time-delay systems (TDS);

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2017147

Filename

4908954