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A barrier certificate is an inductive invariant function which can be usedfor the safety verification of a hybrid system. Safety verification based onbarrier certificate has the benefit of avoiding explicit computation of theexact reachable set which is usually intractable for nonlinear hybrid systems.In this paper, we propose a new barrier certificate condition, calledExponential Condition, for the safety verification of semi-algebraic hybridsystems. The most important benefit of Exponential Condition is that it has alower conservativeness than the existing convex condition and meanwhile itpossesses the property of convexity. On the one hand, a less conservativebarrier certificate forms a tighter over-approximation for the reachable setand hence is able to verify critical safety properties. On the other hand, theproperty of convexity guarantees its solvability by semidefinite programmingmethod. Some examples are presented to illustrate the effectiveness andpracticality of our method.

Exponential-Condition-Based Barrier Certificate Generation for Safety Verification of Hybrid Systems