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Baranyi and Yam proposed the TP model transformation as a new concept in quasi-LPV based control, which plays a central role in the highly desirable bridging between identification and polytopic systems theories. It is also used as a TS fuzzy model transformation. 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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A free MATLAB implementation of the TP model transformation can be downloaded at or an old version of the toolbox is available at MATLAB Central. Be careful, in the MATLAB toolbox the assignments of the dimensions of the core tensor is in the opposite way in contrast to the notation used in the related literature. In some variants of the ToolBox, the first two dimension of the core tensor is assigned to the vertex systems. In the TP model literature the last two. A simple example is given below.