Remote stabilization over fading channels

In this paper, we study the problem of remote mean square stabilization of a MIMO system when independent fading channels are dedicated to each actuator and sensor. We show that the stochastic variables responsible for the fading can be seen as a source of model uncertainty. This view leads to robust control analysis and synthesis problems with a deterministic nominal system and a stochastic, structured, model uncertainty. As a special case, we consider the stabilization over Erasure or drop-out channels. We show that the largest probability of erasure tolerable by the closed loop is obtained from solving a robust control synthesis problem. In more general terms, we establish that the set of plants which can be stabilized by linear controllers over fading channels is fundamentally limited by the channel generated uncertainty. We show that, the notion of mean square capacity, defined for a single channel in the loop, captures this limitation precisely and characterizes equivalence classes of channels within the class of memoryless fading channels.