This paper addresses the problem of data-driven stabilization of continuous-time linear time-invariant systems. The objective is to design a dynamic output-feedback controller directly from a finite input--output trajectory collected during an experiment, without any identification step. The proposed approach applies to general multi-input multi-output systems without a uniform observability index by building on Kreisselmeier's adaptive filter, which acts as an observer of a stabilizable canonical non-minimal realization of the unknown plant. By postprocessing the input-output data through this filter, the stabilization problem is translated into a data-driven linear matrix inequality whose solution yields the feedback gain of a dynamic output-feedback controller. Since the considered non-minimal realization is generally stabilizable rather than controllable, a data-driven state decomposition is introduced to extract the excited coordinates and isolate the stable autonomous modes. The proposed decomposition is then used to implement the controller as a reduced-order system that does not retain the full filter dynamics. Finally, input conditions are provided to guarantee the excitation properties required for data-driven design.