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

Alexander Weber and Gunther Reissig.
Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems.
SIAM J. Control Optim., vol. 52, no. 5, 2014, pp. 2857-2876.

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Abstract:
Necessary and sufficient conditions for convexity and strong convexity, respectively, of connected sublevel sets that are defined by finitely many real-valued

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^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.

BibTeX entry:

@article{WeberReissig14,
  author  = {Alexander Weber and Gunther Reissig},
  title = {Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems},
  journal = {SIAM J. Control Optim.},
  volume = 52,
  number = 5,
  pages = {2857-2876},
  doi = {10.1137/130945983},
  eprint = {1311.4989},
  year = 2014
}

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