In this paper we propose a dynamic output-feedback controller synthesis method for discrete-time linear time-invariant systems. The synthesis goal is to render closed-loop system dissipative with respect to a given generic unstructured quadratic supply rate, while the system dynamics is partially represented by input-state data corrupted by a bounded disturbance. The controller synthesis is performed with respect to all systems which are consistent with the available data, and it is formulated in terms of a linear matrix inequality parametrized by a scalar variable, so that the synthesis can be performed using line search and convex optimization. Within the considered setting, the proposed synthesis procedure is non-conservative in a sense that it is based on conditions which are both necessary and sufficient.

7 pages, 2 figures