Mathematical Problems in Engineering
Volume 7 (2001), Issue 4, Pages 337-353

A hybrid domain analysis for systems with delays in state and control

M. Razzaghi1,2 and H. R. Marzban2

1Department of Mathematics and Statistics, Mississippi State University, Mississippi State, 39762, MS, USA
2Department of Mathematics, Amirkabir University, Tehran, Iran

Received 31 May 2000

Copyright © 2001 M. Razzaghi and H. R. Marzban. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The solution of time-delay systems is obtained by using a hybrid function. The properties of the hybrid functions consisting of block-pulse functions and Chebyshev polynomials are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of delay is introduced. The operational matrices of integration and delay are utilized to reduce the solution of time-delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.