A consideration of the discrete Volterra series

By utilizing multidimensional transforms and the discrete form of the Volterra series it is shown how to analyze a large class of nonlinear sampled-data systems and nonlinear difference equations, presenting the solution in terms of the kernels of the Volterra series. The method is shown to be just as applicable when the discrete system is not quiescent with the interaction between the initial conditions and the driving function evidenced by means of the transition matrix. Several illustrative examples are given, and applications of the method are suggested.