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Hybrid systems have acquired deep attention in research as many systems in industries and laboratories manifest hybrid dynamic behaviors. Optimal control design for hybrid systems exhibits challenges for controlling the interacting continuous and discrete dynamics. A double-tank hybrid system (DTHS) is proposed in this paper with a mixed-integer actuation mechanism. The proposed DTHS aims to control the liquid level of the two tanks simultaneously by a networked hybrid predictive controller. Hybrid frameworks are provided to investigate the system through reachability analysis. An explicit hybrid model predictive control (EHMPC) has been developed to control the levels of the DTHS. Hardware-In-the-Loop (HIL) simulation is performed for assessing the performance of the EHMPC with a hardware real-time networked controller. The networked real-time controller is constructed and implemented using the Node.js frameworks. The simulation and realtime results are presented and discussed to evaluate the hybrid controller performance.