  Computing control invariant sets is paramount in many applications. The
families of sets commonly used for computations are ellipsoids and polyhedra.
However, searching for a control invariant set over the family of ellipsoids is
conservative for systems more complex than unconstrained linear time invariant
systems. Moreover, even if the control invariant set may be approximated
arbitrarily closely by polyhedra, the complexity of the polyhedra may grow
rapidly in certain directions. An attractive generalization of these two
families are piecewise semi-ellipsoids. We provide in this paper a convex
programming approach for computing control invariant sets of this family.
