On a multidimensional<tex>S</tex>-transform and the realization problem for homogeneous nonlinear systems

Abstract

A multidimensional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</tex> -transform, related to the multidimensional Laplace transform, is defined in an algebraic fashion. Some properties of this transform with regard to nonlinear system representation are discussed. In particular the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</tex> -transform representation leads to a solution of a realization problem for stationary, homogeneous, degree <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> nonlinear systems. For ease of exposition the results are presented for the two-dimensional case only.