The problem of H-2 guaranteed cost control and dynamic output-feedback for linear uncertain systems with dissipative uncertainty is addressed. The problem of robust H-2 synthesis has been open for the last two decades. In this payer, a problem of Hz quadratic guaranteed cost control is defined for uncertain systems affected by LTI quadratic dissipative model uncertainty. A necessary and sufficient condition of quadratic stabilizability via output-feedback is derived in terms of two coupled parameter-dependent Riccati equations. Then, a method is given to design controllers which minimize an upper bound for the worst-case H-2 norm of the uncertain system. It therefore assesses a guaranteed level of robust performance where in literature, only nominal performance is ensured in most cases. A reliable numerical iterative procedure based on Riccati solvers and one-dimensional convex parameter search is provided. With this uncertainty modelling and the developped numerical procedure, we hope to reduce the usual conservatism of quadratic designs.