This paper is concerned with H$_{infty}$ controller design methods for descriptor systems with and without time-varying delays in state and control input. The sufficient condition for the existence of an H$_{infty}$ controller and the controller design method are presented by linear matrix inequality (LMI), singular value decomposition, Schur complements, and changes of variables. Since the obtained sufficient condition can be changed to an LMI form by proper manipulations, all solutions including controller gain can be obtained at the same time. Moreover, it is shown that robust H$_{infty}$ controller design problem for parameter uncertain descriptor systems with time-varying delays in state and control input can be solvable using the proposed method.