  In this paper we consider the problem of computing control invariant sets for
linear controlled high-dimensional systems with constraints on the input and on
the states. Set inclusions conditions for control invariance are presented that
involve the N-step sets and are posed in form of linear programming problems.
Such conditions allow to overcome the complexity limitation inherent to the set
addition and vertices enumeration and can be applied also to high dimensional
systems. The efficiency and scalability of the method are illustrated by
computing approximations of the maximal control invariant set, based on the
10-step operator, for a system whose state and input dimensions are 30 and 15,
respectively.
