Criteria of stability and stabilization of singular systems based on generalized positive definite

In this paper we consider the necessary and sufficient conditions for the stability and stabilization of continuous linear time invariant(LTI) singular systems. The results based on generalized positive definite are derived. Two necessary and sufficient conditions of stability, in terms of generalized positive definite of matrices, for the class of linear time invariant singular systems which possess real eigenvalues are presented. The problem of stabilization of singular systems via generalized positive definite is converted into linear matrix inequalities (LMI) techniques. The two new definitions of Hurwitz stable and generalized positive definite of matrix pair are introduced. Based on the same idea, the strict LMI conditions which do not contain equality constraints are derived. Several numerical examples are given to illustrate effectiveness of the presented methods in the paper.