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TP model transformation in control theory
Baranyi and Yam proposed the TP model transformation 〔P. Baranyi (April 2004). "TP model transformation as a way to LMI based controller design". IEEE Transaction on Industrial Electronics 51 (2): 387–400.〕〔P. Baranyi and D. Tikk and Y. Yam and R. J. Patton (2003). "From Differential Equations to PDC Controller Design via Numerical Transformation". Computers in Industry, Elsevier Science 51: 281–297.〕 as a new concept in quasi-LPV (qLPV) based control, which plays a central role in the highly desirable bridging between identification and polytopic systems theories. It is uniquely effective in manipulating the convex hull of polytopic forms, and, hence, has revealed and proved the fact that convex hull manipulation is a necessary and crucial step in achieving optimal solutions and decreasing conservativeness in modern linear matrix inequality based control theory. Thus, although it is a transformation in a mathematical sense, it has established a conceptually new direction in control theory and has laid the ground for further new approaches towards optimality.
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==Key features for control analysis and design==
* The TP model transformation transforms a given qLPV model into a (tensor product type) polytopic form, irrespective of whether the model is given in the form of analytical equations resulting from physical considerations, or as an outcome of soft computing based identification techniques (such as neural networks or fuzzy logic based methods, or as a result of a black-box identification).
* Further the TP model transformation is capable of manipulating the convex hull defined by the polytopic form that is a necessary step in polytopic qLPV model based control analysis and design theories.
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