Safety analysis of linear system with SOS for complex eigenvalues

In this paper we investigate safety verification of linear system. The structure of linear system will be exploited and converted to certain eigenstructure as an emptiness problem for a semi algebraic set. Sum of square (SOS) is emploited to check emptiness of of the set defines by polynomial inequalities which can be computed by semidifinite programming. A special consideration is to investigate safety problem of linear system with complex eigenvalues.