This paper investigates the design of an “extended” H2 output feedback controller for continuous descriptor systems. In such problem, the controller, which is described within descriptor framework, has to satisfy simultaneously two conditions: 1-The closed-loop is admissible and has minimum H2 norm. 2-Only the internal stability of a part of the generalized closed-loop is sought. In such case, the standard H2 output feedback control problem for descriptor systems cannot be solved. An explicit characterization of the optimal solution, based on two generalized algebraic Riccati equations and two structured generalized Sylvester-type equations, is given. A numerical example is given to illustrate the applicability of the proposed results.