This note is concerned with the problem of the so-called quadratic normalization and stabilization via both proportional and derivative state feedback (PDSF) and proportional and derivative output feedback (PDOF) for uncertain descriptor systems with norm-bounded perturbations. Necessary and sufficient conditions are presented in terms of linear matrix inequalities (LMIs) or quadratic matrix inequalities (QMIs), by using a simple idea of changing the problem to the corresponding stabilization problem of an augmented uncertain system.