S.O.S. for safety

Verification of continuous systems remains one of the main obstacles in the safety verification of hybrid systems. In this paper, by exploiting the structure of linear dynamical systems, we convert the exact safety verification of linear systems with certain eigen-structure as an emptiness problem for a semi-algebraic set. Sum of squares (SOS) decomposition is then employed to check emptiness of the set defined by polynomial equalities and inequalities which can be effectively computed by semidefinite programming.