Abstract: The problem of guaranteed cost control was dealt with for a class of uncertain descriptor systems, whose class is with parameter uncertainties and norm-bounded. The purpose of the problem was to design a state feedback controller such that, for all admissible uncertainties, the closed-loop descriptor systems keep regular, impulse-free and stable. At the same time an adequate level of a quadratic cost index can be guaranteed. A sufficient condition for the existence of guaranteed cost controllers was derived. It was shown that a group of linear matrix inequalities provided a parameterized representation of guaranteed const controllers.