Mean square stabilization of LTI systems over packet-drop networks with imperfect side information

In this paper, we consider the problem of designing a Mean square stabilizing controller for a SISO plant over drop-out actuator and sensor channels. Previous work has derived limitations on the maximal drop-out probability tolerable when a perfect feedback (service) channel is allowed to carry acknowledgements from the actuator receiver to the controller. In this paper, we assume the service channel is imperfect and also subject to drop-outs. We consider two cases: one in which the service channel communicates the receiver acknowledgements, the other in which it communicates the actuator channel state. We derive tradeoff curves relating the minima] quality of service required for stabilization with the percentage of drop-outs in the service channel. The theoretical tradeoff curve is in conjunction with the one obtained from an experimental setup.