Possibilities for Representing the Shape and Size of Polytopes when Applying the Tp Transition

Abstract:

One of the most popular controller designs in control engineering is the so-called linear matrix inequality (LMI) method. In this method, the optimization is defined within a convex polytope, for which the first step is to define the convex polytope describing the problem. With the tensor product model transformation, we can directly derive such convex hulls from the linear parameter variable (LPV, qLPV) description of the nonlinear system, for example SNNN, IRNO, CNO. A transition can be formed between them, with which an infinite number of polytope representations can be produced for a system. The literature shows that narrower hulls (CNO) result in smaller control signals, which are easier to implement in practice. An easy-to-understand representation of the size of these polytopes is currently still a challenge in the literature. There is also a physical content behind them, so the norms known in mathematics are not sufficiently representative. This research presents the currently known representation techniques and their limitations.

• Periodical: Advances in Science and Technology (Volume 181)
• Pages: 259-265
• DOI: https://doi.org/10.4028/p-RA6j9q
• Online since: August 2026
• Authors: Dániel Nemes*, Sándor Hajdu
• Keywords: Convex Hull, LMI, Polytopic Modeling, TP Model Transformation

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