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This paper introduces control barrier functions for discrete-time systems, which can be shown to be necessary and sufficient for controlled invariance of a given set.
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Construction of parametric barrier functions for dynamical systems using interval analysis
A. Djaballah, A. Chapoutot, M. Kieffer, and O. Bouissou · 2017
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Discrete control barrier functions for safety-critical control of discrete systems with application to bipedal robot navigation
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Control barrier functions for signal temporal logic tasks
L. Lindemann and D.V Dimarogonas · 2018
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Boolean composability of constraints and control synthesis for multi-robot systems via nonsmooth control barrier functions
P. Glotfelter, J. Cortés, and M. Egerstedt · 2018
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