Stabilization over additive white noise forward and feedback channels

In this paper, we study the problem of stabilizability of LTI systems over both the forward (from the controller to the plant) and feedback (from the sensor to the controller) channel. We adopt the additive white noise (AWN) channel with a prescribed power constraint as our channel model. For first order systems, we derive explicitly the necessary and sufficient conditions for stabilizability and show the tradeoff between the minimum signal-to-noise ratio (SNR) required for the forward and feedback channel. We also show explicitly that the use of two-parameter controller in this problem assumes better performance.