The descriptor system model has a high ability in representing dynamical systems. It can preserve physical parameters in the coefficient matrices, and describe the dynamic part, static part, and even the improper part of the system in the same form. The design of mixed $H_{2}/H_{infty}$ controllers for linear time-invariant descriptor systems is considered in this paper. Firstly, an $H_2$ and $H_{infty}$ synthesis problems fur a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, we show that the existence of a mixed $H_2/H_{infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_2$ norm bound of the first channel less than ${gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables.