Integral transforms for a class of time-varying linear systems

Abstract

This paper presents an extension of the transform method to systems having parameters which vary with time. By using the general λ domain approach suggested by Zadeh for the analysis and synthesis of linear time-varying systems, a system function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(\lambda)</tex> independent of time may be defined for the linear system. Such a system function has many of the advantages of that obtained for stationary systems using the Laplace transformation. By making <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(\lambda)</tex> a ratio of polynomials in the complex variable λ the pole-zero synthesis technique used for fixed systems may be applied to the time-varying case as well. Recently, a "building block" for the synthesis of a class of time-varying systems was suggested by Kilmer and Johnson. A similar building block for systems with exponentially varying coefficients is suggested in this paper.