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Barrier Function Certificates for Forward Invariance in Hybrid Inclusions

  • Author(s): Maghenem, M;
  • Sanfelice, RG
  • et al.
Abstract

This paper proposes barrier functions for the study of forward invariance in hybrid systems modeled by hybrid inclusions. After introducing an appropriate notion of a barrier function, we propose sufficient conditions to guarantee forward invariance properties of a set for hybrid systems with nonuniqueness of solutions, solutions terminating prematurely, and Zeno solutions. Our conditions involve infinitesimal conditions on the barrier certificate and Minkowski functionals. Examples illustrate the results.

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