Analysis of time-delay systems via Walsh functions

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Abstract
This paper introduces a new set of operational matrices for delay and advance via Walsh functions. These matrices, along with the well known operational matrix for integration, reduce the calculus of a large class of delay (or advance) systems to an algebra approximate in the sense of least squares. Some useful properties and applications of the proposed matrices are discussed. In particular, a method of integrating delay differential equations is extensively illustrated. With the single term Walsh series method (Prasada Rao et at. 1980) the computation becomes very simple. In addition to the piecewise constant solutions, discrete solutions can also be computed. Some features of the paper are : (i) a technique to include carry over effects ; and (ii) an analysis of the error and stability of computations. Several illustrative examples are included and the results are compared with those obtained by certain conventional methods.

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