  In this paper, we present a geometric approach for computing the controlled
invariant set of a continuous-time control system. While the problem is well
studied for in the ellipsoidal case, this family is quite conservative for
constrained or switched linear systems. We reformulate the invariance of a set
as an inequality for its support function that is valid for any convex set.
This produces novel algebraic conditions for the invariance of sets with
polynomial or piecewise quadratic support function. We compare it with the
common algebraic approach for polynomial sublevel sets and show that it is
significantly more conservative than our method.
