ABSTRACT
In the prevailing literature, one can find a considerable number of papers on tractable and systematic manipulation of linear matrix inequalities (LMIs) aimed at achieving the best control performance. Most of these works are devoted to the derivation of new and more powerful LMIs to facilitate enhanced control system design. In contrast, relatively little attention has been given to the transformation of given models into proper polytopic, affine model representations in order to influence the feasibility and effectiveness of the applied LMIs, and hence the resulting control performance. In this regard, we note that recent papers have actually shown that different constructions of the system matrix in the quasi-linear parameter-varying (qLPV) model will lead to considerably different LMI solutions [HL96]. The purpose of this section is thus to show that the optimization of the control performance must include the manipulation of the convex hull in addition to the construction of LMIs, and that the tensor product (TP) model transformation as described here in this book offers a systematic solution.
