P th‐order inverse of the Volterra series for multiple‐input multiple‐output non‐linear dynamic systems

Abstract

A method to determine the pth-order inverse of the Volterra series of multiple-input multiple-output non-linear dynamic systems is presented; it combines time- and frequency-domain techniques to determine the Volterra series of the inverse as a function of the forward system's Volterra series. The method can be used for continuous and discrete time systems. Each operator of non-linear order n of the inverse is a function of the forward system's operators of non-linear order n and lower. It is shown that the pth-order post-inverse is equal to the pth-order preinverse. For the special case that there are no linear cross terms and that the linear memory effects are negligible the kernels of the forward and inverse models are approximately the same. In an example, an approximate inverse model of a model of a concurrent dual band radio frequency amplifier is derived.