HOSVD-based canonical form of TP functions and qLPV models


Based on the key idea of higher-order singular value decomposition in tensor algebra, Baranyi and Yam proposed the concept of HOSVD-based canonical form of TP functions and quasi-LPV system models. Szeidl et al. proved that the TP model transformation is capable of numerically reconstructing this canonical form.
Related definitions can be found here. Details on the control theoretical background can be found here.
A free MATLAB implementation of the TP model transformation can be downloaded at or at MATLAB Central .

Existence of the HOSVD-based canonical form

Assume a given finite element TP function:
where. Assume that, the weighting functions in are othonormal for. Then, the execution of the HOSVD on the core tensor leads to:
Then,
that is:
where weighting functions of are orthonormed and core tensor contains the higher-order singular values.

Definition

;HOSVD-based canonical form of TP function
, in vector
form an orthonormal set:
where is the Kronecker delta function
.