Analysis of time-varying delay systems by hybrid of block-pulse functions and biorthogonal multiscaling functions

Abstract

This paper proposes new effective methods for analysis of time-varying delay systems using new hybrid functions. The excellent properties of the hybrid functions which consist of block pulse functions and biorthogonal multiscaling functions are presented. We utilise operational matrices of product, delay and integration to reduce the solution of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

Keywords:

• delay systems
• hybrid functions
• block-pulse function
• biorthogonal multiscaling functions
• cubic Hermite splines
• operational matrix

Acknowledgements

The authors are grateful to both referees for their comments and suggestions which have improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.