Nonlinear sampled-data system analysis by multidimensional z transforms

The paper is concerned with the analysis by multidimensional z transforms of sampled-data nonlinear systems, for which the continuous representation is a Volterra functional series. A sequential process based on simple procedures is proposed for obtaining the multidimensional z transform of a nonlinear-system kernel from the multidimensional Laplace transform of the kernel. For nonlinear systems cascaded with a data-hold device, a method is developed by which the multidimensional z transform of the kernel of the cascade combination may be obtained by applying the process to a derived multidimensional Laplace transform. A sequential process for obtaining the sampled-data output of a nonlinear system with a given sampled-data input is also described, and extended to the case of asynchronous input-output sampling by means of a multidimensional modified z transformation.