PROJECT TITLE :

Converse Barrier Certificate Theorems

ABSTRACT:

This technical note shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a connected result by assuming that the dynamical system has neither singular points nor closed orbits. In this technical note, we tend to redefine the quality notion of safety to suits dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a range of illustrative examples.