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Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control.
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H. Kong, F. He, X. Song, W. Hung, and M. Gu, “Exponential-condition-based barrier certificate generation for safety verification of hybrid systems,” in CAV¡¯13, volume 8044 of LNCS . Springer, 2013, pp. 242–257
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