Exact reconstruction of HOSVD based TP models from sampled data

This paper investigates the exact reconstruction of finite element HOSVD based TP models from sampled data over a regular grid. A special class of functions is considered which is reconstructible with given interpolation method from the sampled data. It is shown that the HOSVD based TP model form of these functions are reconstructible.

I. Introduction

Tensor product (TP) model transformation is a recently proposed controller design method for Linear Parameter Varying systems [1]. Its main idea is to define a Higher Order Singular Value Decomposition (HOSVD) based canonical form for these LPV systems, which can approximately represented by data arrays, which are easy to manipulate to formulate various control problems. This canonical form is derived by sampling a multivariable function and assuming that the samples represent the function well enough. In this paper we investigate when it is possible that the sampling represent the function exactly and allows exact reconstruction of the HOSVD based TP model form.