Robust D stabilization of singular systems with polytopic uncertainties

The robust D stabilization problem is considered for singular systems with polytopic uncertainties in this paper. Both the derivative matrix E and the state matrix A are with uncertainties, under the assumption that the rank of matrix E is constant. Firstly, with the introduction of some free matrices, a new dilated LMI condition for the singular system to be D stable is proposed, based on which, the robust D stable problem is solved, and a sufficient condition for the closed system to be robust D stabilizable is obtained. The desired state feedback controller is given in an explicit expression. Numerical examples show the efficiency of the obtained approach.