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This paper addresses the robust H2 guaranteed cost control of continuous-time Markov jump linear systems, in the dynamic output feedback scenario. It is assumed that the jump process takes values in a countably infinite set. In the finite case, an adjoint approach to the robust control of MJLS in face of linear structured uncertainty is developed. A numerical example, regarding the robust control of the coupling between two damped oscillators, illustrates the applicability of the proposed results.