Darboux-type barrier certificates for safety verification of nonlinear hybrid systems
Xia Ling Zeng, Lin Wang, Zhengfeng Yang, Xin Chen, Lilei Wang · 2016
Benefit from less computational difficulty, barrier certificate based method has attracted much attention in safety verification of hybrid systems. Barrier certificates are inherent existences of a hybrid system and may have different types. A set of well-defined verification conditions is a prerequisite for successfully identifying barrier certificates of a specific type. Therefore, how to define verification conditions that can identify barrier certificates invisible to existing conditions becomes an essential problem in barrier certificate based verification. This paper proposes a set of verification conditions that helps to construct a new type of barrier certificate, namely, the Darboux-type barrier certificate made of Darboux polynomial. The proposed verification conditions provide powerful aids in non-linear hybrid system verification as the Darboux-type barrier certificates can verify systems that may not be settled by existing verification conditions.