A new method for the design of fixed-order dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented in this paper. Sufficient conditions for the stability, H2 and induced L2 performance of a given LPV system are given through a set of Linear Matrix Inequalities (LMIs) and exploited for design. Controller parameters appear directly as decision variables in the convex optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the improvement of the control system performance.