Analytical solution of a system of homogeneous delay differential equations via the Lambert function

Author

Asl, Farshid Maghami ; Ulsoy, A. Galip

Author_Institution

Dept. of Mech. Eng. & Appl. Mech., Michigan Univ., Ann Arbor, MI, USA

Volume

4

fYear

2000

fDate

2000

Firstpage

2496

Abstract

A new approach to obtain an analytic solution for delay differential equations (DDE) based on the concept of Lambert functions is presented in this paper. The similarity of the results with the concept of the state transition matrix in ordinary differential equations enables the approach to be used for general classes of linear delay differential equations including the matrix form of DDE. Stability criteria for delay equations in different cases are studied and the results are presented in the paper

Keywords

delay-differential systems; differential equations; matrix algebra; stability criteria; DDE; Lambert function; homogeneous delay differential equations; linear delay differential equations; ordinary differential equations; stability criteria; state transition matrix; Control system synthesis; Delay effects; Delay systems; Differential equations; Frequency; Laplace equations; Mechanical engineering; Systems engineering and theory; Temperature control; Transmission line matrix methods;

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.2000.878632

Filename

878632