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arXiv · 2610.41966

On Universal Minkowski Classes of Polytopes: Theory and Applications

Boris Houska·Matthias A. Müller·Mario Eduardo Villanueva
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Abstract

This paper establishes the existence, in every dimension, of universal Minkowski classes of configuration-constrained polytopes, with direct applications to set-theoretic control. For any prescribed accuracy, such a class contains an approximation of every compact convex set to that accuracy and admits a jointly affine parameterization of facets and vertices. The construction is explicit and relies on a combinatorial averaging procedure that produces minimal configuration enclosures. In control, these polytopic templates enable convex reformulations of otherwise non-convex problems, including invariant-set computation and control Lyapunov function design. Tutorial examples illustrate both the geometric construction and its control applications.

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Boris Houska, Matthias A. Müller, Mario Eduardo Villanueva. 2026-10-30. On Universal Minkowski Classes of Polytopes: Theory and Applications. https://arxiv.org/abs/2610.41966

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