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arXiv · 1311.4989

Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems

Alexander Weber·Gunther Reissig
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Abstract

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 to over-approximate attainable sets when strong convexity is present.

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Alexander Weber, Gunther Reissig. 2013-11-20. Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems. https://doi.org/10.1137/130945983

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