Premium
On the full and block‐decoupling of nonlinear functions
Author(s) -
Dreesen Philippe,
Ishteva Mariya,
Schoukens Johan
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510352
Subject(s) - jacobian matrix and determinant , univariate , decoupling (probability) , nonlinear system , set (abstract data type) , multivariate statistics , representation (politics) , mathematics , algorithm , computer science , engineering , statistics , physics , control engineering , quantum mechanics , politics , law , political science , programming language
We review a method that decouples multivariate functions into linear combinations of a set of univariate (or simpler multivariate) functions of transformed variables. In this way the given nonlinear multiple‐input‐multiple‐output function is decoupled into a structure having simpler parallel internal branches that are linked by linear transformations to the original inputs and outputs. The procedure collects first‐order information by evaluating the Jacobian matrix of the given function in a set of points. These matrices are stacked into a three‐way tensor, whose decomposition reveals the decoupled representation. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)