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Classical and Strong Convexity of Sublevel Sets and Application to Attainable Sets of Nonlinear Systems
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
doi:10.1137/130945983
fatcat:mlrgpm6sn5euxd5sawmjbi5bdi