Computing control invariant sets is paramount in many applications. The families of commonly used for computations are ellipsoids and polyhedra. However, searching a set over the family conservative systems more complex than unconstrained linear time systems. Moreover, even if may be approximated arbitrarily closely by polyhedra, complexity polyhedra grow rapidly certain directions. An attracti...

In [1] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals (e.g., real semialgebraic or subanalytic sets), and having connected intersections with all translated coordinate cones in Rn. In this paper we develop this theory further by defining monotone functions and maps, and studying their fundamental geometric properties. We prove several equ...

We provide a Hilbert-Mumford Criterion for actions of reductive groups G on Q-factorial complex varieties. The result allows to construct open subsets admitting a good quotient by G from certain maximal open subsets admitting a good quotient by a maximal torus of G. As an application, we indicate how to obtain all invariant open subsets with good quotient for a given G-action on a complete Q-fa...

We study interior operators and interior structures in a fuzzy setting.We investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.