In this article, the problem of fixed-order $H_2$ controller design for continuous-time polytopic systems is investigated. It is assumed that the uncertain parameters appear in the state space realization of the system. A convex set of fixed-order $H_2$ controllers is presented by introducing a slack matrix variable which decouples the Lyapunov variables and the controller parameters. Taking advantage of this feature, we can readily design a robust fixed-order controller for a polytopic system with non-common Lyapunov variables. An optimization problem is presented for computing the slack variables using an initial controller selected by the designer. Additionally, to improve the obtained performance, a procedure is provided to reduce the dependency of the method on the initial controller. The design conditions are in terms of solutions to a set of linear matrix inequalities. Numerical examples demonstrate the effectiveness of the proposed approach.