ABSTRACT
The key idea of tensor product (TP) model transformation was first introduced in [BTYP03], [Bar04], [BVK05]. The objective of the transformation is to numerically convert any given quasi-linear parameter-varying (qLPV) model (2.1) into a finite element TP type polytopic model type form (Definition 2.4) in the parameter space Ω: (
x˙ y
) = S(p)
( x u
) =
( S N
n=1 wn(pn)
) ( x u
) . (3.1)
Particularly, the TP model transformation generates a canonical form as an intermediate step during the process. This canonical form, to be discussed in detail in Chapter 4, will enable the incorporation and manipulation of different types of TP model convexity as defined in Chapters 2 and 6. Given that the ensuing controller design feasibility and performance are very sensitive to the type of convexity attained, the ability to carry out such manipulations in the design process is highly desirable. The transformation also allows the determination of exact and nonexact TP model representations (Definition 2.8) for the given qLPV model using only a minimal number of components. In the nonexact case, a trade-off study between the number of components and the accuracy of the resulting TP model is also provided.
