Limitations in remote stabilization over unreliable channels without acknowledgements

We consider the remote control of linear systems using unreliable communication channels where transmitted messages may be randomly lost and aim at clarifying the limitations arising there. In particular, we study the case without acknowledgement messages from the actuator to the remote controller regarding the arrival of the control input. It is shown that for a class of plants, stabilization is possible if and only if the loss rates satisfy critical bounds which have been known in the literature when acknowledgements are available. We present a constructive proof employing a nonlinear controller that makes control input estimation.