Definition of the HOSVD based canonical form of polytopic dynamic models

Abstract

The main objective of the paper is to introduce how the concept of tensor HOSVD can be carried over to the TP (tensor product) dynamic models, namely, how we can define and generate the "HOSVD like" decomposition of linear parameter varying (LPV) dynamic models. We term this decomposition as HOSVD based canonical form of TP model or polytopic model form. The key idea and the basic concept of this decomposition was proposed with the TP model transformation based control design methodology. The novelty of this paper is to present the mathematical background of this concept. The paper shows convergency theorems how the TP model transformation is capable of reconstructing this HOSVD based canonical form numerically. The proofs of the theorems are lengthy, therefore they are omitted. The paper also presents numerical examples to show the applicability, efficiency and uniformity of the numerical reconstruction