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

This paper considers the robust stabilization problem for linear continuous -time descriptor systems with norm-bounded perturbations in matrix E. We sh ow that if the problem has a solution, then the perturbations must not incr ease the rank of E. Under the assumption that the rank of E with uncertaint ies is always equal to the rank of E without uncertainties, the problem und er consideration falls into two cases. For the first case, a complete solut ion 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.