Approximating state sets using circumscribing polyhedron with fewer facets

A polyhedron can be described using a set of linear constraints that bound the polyhedron. This paper considers the problem of approximating a polyhedron with a circumscribing polyhedron with fewer constraints. We discuss three methods to find such a circumscribing polyhedra, and compare the resulting approximation errors using sets of randomly generated polyhedra. The work is motivated by the problem of approximating state estimate sets for a class of uncertain dynamic systems.