Robust stabilization via state feedback for descriptor systems with uncertainties in the derivative matrix

Abstract

This paper considers the robust stabilization problem for linear continuous-time descriptor systems with norm-bounded perturbations in matrix E. We show that if the problem has a solution, then the perturbations must not increase the rank of E. Under the assumption that the rank of E with uncertainties is always equal to the rank of E without uncertainties, the problem under consideration falls into two cases. For the first case, a complete solution in terms of a necessary and sufficient condition is given for quadratic stabilization. For the other case, a necessary condition and a sufficient condition are presented.