This paper provides a new robust control synthesis method for linear uncertain multivariable discrete-time systems subject to the ellipsoidal parametric uncertainty. This type of parametric uncertainty is delivered by classical prediction error identification methods in a full-order model structure. The uncertainty is represented by linear fractional transformation. Fixed-order H-2 and H-infinity control design problems are formulated in terms of solutions to a set of dilated linear matrix inequalities. The control designs build on quadratically parameter-dependent Lyapunov functions. Flexible structures for the auxiliary variables are introduced to improve the performance and reduce the conservatism related to the fixed-order controller synthesis. The employed structures may be updated by a proposed iterative procedure. Numerical examples show the effectiveness of the proposed method.