Analysis of time-delay systems using the Galerkin method

Abstract

This paper is concerned with the analysis of a time-varying, variable time-delay system using the Galerkin method. The approximate solution is expanded in a set of shifted Legendre polynomials with unknown expansion coefficients. A delay matrix is derived to manipulate the time delay. The original delay-differential equation is converted to a set of algebraic equations through setting the weighted integrals of the residual to zero. An approximate shifted Legendre series solution to the time delay system is thus obtained by solving the resultant algebraic equations. Numerical results are provided to illustrate the applicability of the method.