A new method for the design of fixed-structure dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, $\mathscr{H}_2$ and induced $l_2$-norm performance of a given LPV system are represented through a set of Linear Matrix Inequalities (LMIs). These LMIs are used in an iterative algorithm with monotonic convergence for LPV controller design. Extension to the case of uncertain scheduling parameter value is considered as well. Controller parameters appear directly as decision variables in the optimization 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 optimization scheme used for the improvement of the control system performance.