This paper is concerned with a non-standard multi-objective state feedback control problem for continuous descriptor systems. In this problem an output is to be regulated asymptotically with presence of an infinite-energy exo-system, while a desired H2 performance from a finite external disturbance to a tracking error has also to be satisfied. Thanks to the descriptor framework, not only unstable but also nonproper behaviors can be treated. A parametrization of all optimal dynamic and static controllers solving the proposed multi-objective control problem is given. Moreover, an application to the non-standard LQR problem is investigated. A numerical example shows the efficiency of the proposed results.