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