Safety analysis of linear systems with complex eigenvalues using SOS

This paper considers safety analysis of linear systems. The structure of linear systems will be investigated and converted to certain eigenstructure as an emptiness problem for a semi algebraic set. Sum of square (SOS) is utilized to check the emptiness of the set defined by polynomial equalities and inequalities which can be computed by semi definite programming. A special consideration is investigating safety problem of linear systems with complex eigenvalues. The results are then applied to the safety problem for a reduced model of longitudinal mode of a small scale helicopter. © 2013 by IJIR (CESER Publications).