On a multidimensionalS-transform and the realization problem for homogeneous nonlinear systems

A multidimensional
S
-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
S
-transform representation leads to a solution of a realization problem for stationary, homogeneous, degree
n
nonlinear systems. For ease of exposition the results are presented for the two-dimensional case only.