This paper deals with the finite time control of linear systems subject to exogenous inputs. Previous works establish sufficient conditions for finite time stabilization via state feedback in terms of LMIs based optimization. An approach to solve the more challenging output feedback problem has been recently proposed in the literature. The drawback of this last result is that the controller design is performed in two phases (static state feedback and observer) and therefore it does not exploit the possibilities offered by the design performed in one step. In this context the main result of this paper is a sufficient condition guaranteeing the finite time stabilizability via output feedback; such condition, which looks at the dynamic controller as a whole, can be converted into a feasibility problem involving LMIs. An example illustrates the proposed methodology.