This paper considers H∞ optimal control of LTI systems where the loop is closed over TCP-like lossy networks. Following a game theoretic formulation of the problem, we first obtain an explicit H ∞ controller. We then analyze the infinite-horizon behavior of the H∞ controller. In particular, we provide necessary and sufficient conditions in terms of the packet drop probability and the H ∞ disturbance attenuation parameter under which the optimal controller is unique and stabilizes the closed-loop system in the mean-square sense. It is also shown that these conditions are coupled; therefore, they cannot be determined independently. A numerical example is presented to illustrate the main results.