Classical and Strong Convexity of Sublevel Sets and Application to Attainable Sets of Nonlinear Systems

Alexander Weber, Gunther Reissig
2014 SIAM Journal of Control and Optimization  
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued C^1,1-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
more » ... is a novel method to over-approximate attainable sets when strong convexity is present.
doi:10.1137/130945983 fatcat:mlrgpm6sn5euxd5sawmjbi5bdi