This paper studies optimal control problems associated to networked systems. In particular, we focus on a case where a multiple-input multiple-output (MIMO) plant is controlled over a channel subject to multiple signal-to-noise ratio (SNR) constraints. For this setup, we establish necessary and sufficient conditions for the existence of static state-feedback controllers that stabilize the plant in a mean square sense. Such conditions are given in terms of a convex optimization problem involving linear matrix inequalities (LMIs). An optimal design procedure is also presented. As an application of our results, we study a class of networked systems closed over erasure channels. © 2011 IFAC.