Open Accessp th‐order inverse of the Volterra series for multiple‐input multiple‐output non‐linear dynamic systems
Author(s) -
Rönnow Daniel
Publication year - 2018
Publication title -
iet circuits, devices and systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.251
H-Index - 49
eISSN - 1751-8598
pISSN - 1751-858X
DOI - 10.1049/iet-cds.2017.0447
Subject(s) - volterra series , inverse , mathematics , inverse system , series (stratigraphy) , linear system , function (biology) , control theory (sociology) , nonlinear system , mathematical analysis , computer science , physics , paleontology , geometry , control (management) , quantum mechanics , evolutionary biology , artificial intelligence , biology
A method to determine the p th‐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 p th‐order post‐inverse is equal to the p th‐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.