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This paper addresses the H∞ dynamic output feedback control design problem of discrete-time Markov jump linear systems. Under the mode-dependent assumption, which means that the Markov parameters are available for feedback, the main contribution is on the complete characterization of all full order proper controllers such that the H∞ norm of the closed loop system remains bounded by a given pre-specified level, yielding the global solution to the corresponding mode-dependent optimal control design problem, expressed in terms of pure linear matrix inequalities. LMIs. A practical application, consisting the networked control of a vehicle platoon using measurement signals transmitted in a Markov channel, as initially proposed in Seiler, P and Sengupta, R., (2005), is considered.