On Estimating the Degree of Nonconvexity of Reachable Sets of Control Systems

We study the properties of reachable sets of control systems that are linear in control. For the reachable sets of a certain class of such systems, we estimate the growth of their degree of nonconvexity $\alpha $ over time. As an auxiliary result, we establish a relationship between $\alpha $-sets and weakly convex sets in the sense of Vial.