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In this paper we discuss how to generate inductive invariants for safetyverification of hybrid systems. A hybrid symbolic-numeric method is presentedto compute inequality inductive invariants of the given systems. A numericalinvariant of the given system can be obtained by solving a parameterizedpolynomial optimization problem via sum-of-squares (SOS) relaxation. And amethod based on Gauss-Newton refinement and rational vector recovery isdeployed to obtain the invariants with rational coefficients, which exactlysatisfy the conditions of invariants. Several examples are given to illustrateour algorithm.

Exact Safety Verification of Hybrid Systems Using Sums-Of-Squares Representation