Analysis and synthesis of dynamic systems containing time delays via block-pulse functions

Abstract

This paper presents a method of numerically integrating differential equations containing time delays via block-pulse functions. The resulting solutions are piecewise constant with minimal mean-square error. The method is based on the use of a newly developed ‘delay matrix’ and enlarges the scope of useful applications of block-pulse functions to problems of dynamic systems. Examples of linear and nonlinear delay systems are included.