| Popis: |
A methodology for safety verification of nonlinear systems using barrier certificates has been proposed recently. The condition was stated in a sufficiency form: if there exists a barrier certificate, then the system is safe, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. Using the concepts of convex duality and density functions, in this paper we derive a converse statement for barrier certificates, showing that in a quite general setting the existence of a barrier certificate is also necessary for safety. |
