Simultaneous Reduction and Expansion of Multidimensional Laplace Transform Kernels

Abstract

Application of Laplace transforms in linear systems analysis has many well established merits. Analogously, multidimensional Laplace transforms can be employed in the analysis of nonlinear analytic systems to provide similar benefits, including explicit input–output relationships. At present, one of the most serious drawbacks to the use of multidimensional transforms lies with the difficulty in reducing multidimensional kernels during inverse transformation. Herein, simplified reduction and expansion techniques for multidimensional inverse transformation will be presented. The labor involved in their application is comparable to that of familiar inverse transformation through use of Heaviside’s expansions. Examples will help to clarify the techniques.