This paper presents a sliding mode dynamic output feedback controller design for Markovian jump systems under a communication network. For the inaccessible states and uncertain parts of Markovian jump systems, a novel integral-type sliding mode output feedback controller combined with system states and dynamic controller states is proposed. An event-triggered mechanism is introduced to reduce network bandwidth and resources requirements. The augmented dynamic system and complete control framework are presented together. The reachability of the novel integral-type sliding mode is proved. Then, based on delay-dependent Lyapunov functions, free-weighting matrices, and a singular value decomposition approach, a less conservative sufficient condition is proposed to ensure exponential stability with a weighted $\mathcal {L}_{2}$ - $\mathcal{ L}_{\infty}$ disturbance performance. Finally, a numerical and a DC-DC switched boost converter circuit simulations that verify the feasibility and effectiveness of the proposed controller are presented.