Algebraic conditions for stability of linear singular systems

Stability properties of arbitrary solutions of linear singular systems are considered. Solution properties of nonhomogeneous systems are investigated on the basis of properties of an associated homogeneous system. The relationship of nonhomogeneous and homogeneous singular systems in terms of stability is investigated and clarified. Algebraic conditions for stability and boundedness of linear singular systems are derived in terms of conditions on system matrices. The algebraic conditions are independent of the system index and smoothness of the forcing term in the nonhomogeneous system.