Convex analysis of invariant sets for a class of nonlinear systems

We study the invariance of the convex hull of an invariant set for a class of nonlinear systems satisfying a generalized sector condition. The generalized sector is bounded by two symmetric functions which are convex/concave in the right half plane. In a previous paper, we showed that, for this class of systems, the convex hull of a group of invariant level sets (ellipsoids) of a group of quadratic Lyapunov functions is invariant. This paper shows that the convex hull of a general invariant set needn´t be invariant, and that the convex hull of a contractively invariant set is, however, invariant.