Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series

Abstract

A method for finding the solution of linear time-varying multi-delay systems using a hybrid function is proposed. The properties of the hybrid functions which consist of block-pulse functions plus Taylor series are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration, delay and product are presented and are utilized to reduce the solution of multi-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.