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In this paper, we consider the $H_{\infty}$ optimal control problem for aMarkovian jump linear system (MJLS) over a lossy communication network. It isassumed that the controller communicates with each actuator through a differentcommunication channel. We solve the $H_{\infty}$ optimization problem for aTransmission Control Protocol (TCP) using the theory of dynamic games andobtain a state-feedback controller. The infinite horizon $H_{\infty}$optimization problem is analyzed as a limiting case of the finite horizonoptimization problem. Then, we obtain the corresponding state-feedbackcontroller, and show that it stabilizes the closed-loop system in the face ofrandom packet dropouts.

$H_{\infty}$ Optimal Control of Jump Systems Over Multiple Lossy Communication Channels