TP model based canonical and various convex manipulations for LPV models

Linear Parameter Varying (LPV) representations of dynamic models and Linear Matrix Inequality (LMI) based feasibility play a central role in modern control theory. The PI introduced a definition of the Higher Order Singular Valued Decomposition (HOSVD) based canonical form of LPV models, which is the first unique representation of LPV models, and developed the Tensor Product (TP) model transformation, which is capable of numerically reconstructing this canonical form. The TP model transformation is also capable of generating various convex polytopic representations of LPV models, upon which LMI-based analysis and design are immediately applicable. This HOSVD-based canonical form and the TP model transformation based methodology of the uniform and automatic generation of convex polytopic models are new in control theory, and lead to new analysis and design concepts in various aspects. The need for such concepts is supported by the conjecture that the manipulation of the type of the convex hull would in many cases be more powerful in multi-objective control design than the analytical derivations of further LMI systems.