Sufficient conditions for closed-loop control over a Gaussian relay channel

The problem of remotely stabilizing a noisy first order linear time invariant system with an arbitrary distributed initial state over a general half-duplex white Gaussian relay channel is addressed. We propose to use linear and memoryless communication and control strategies which are based on the Schalkwijk-Kailath coding scheme. By employing the proposed scheme over the general half-duplex Gaussian relay channel, we derive sufficient conditions for mean square stability of the noisy first order linear time invariant dynamical system.