6 research outputs found
Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems
Necessary and sufficient conditions for convexity and strong convexity,
respectively, of sublevel sets that are defined by finitely many real-valued
-maps are presented. A novel characterization of strongly convex sets
in terms of the so-called local quadratic support is proved. The results
concerning strong convexity are used to derive sufficient conditions for
attainable sets of continuous-time nonlinear systems to be strongly convex. An
application of these conditions is a novel method to over-approximate
attainable sets when strong convexity is present.Comment: 20 pages, 3 figure