Solution of piecewise constant delay systems using hybrid of block-pulse and Chebyshev polynomials

Abstract

An efficient numerical method for finding the solution of piecewise constant delay systems is presented. The method is based upon hybrid of block-pulse functions and Chebyshev polynomials. The operational matrix of delay is constructed. The properties of hybrid functions together with the operational matrices of integration, delay and product are used to convert the delay differential equation to an algebraic equation, thus greatly simplifying the problem. The method is easy to implement and yields very accurate results. The validity and applicability of the proposed method are demonstrated by considering different types of delay systems. © 2010 John Wiley & Sons, Ltd.