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Rate Sufficient Conditions for Closed-loop Control over Half-duplex AWGN Relay Channels

The problem of remotely controlling an unstable noiseless linear time invariant system over noisy half-duplex relay channels with average power constraints is considered. For information transmission, we propose a coding scheme based on the Schalkwijk-Kailath scheme. Therefore, we derive conditions on rate which are sufficient for mean square stability of the linearly controlled LTI system over non-orthogonal, orthogonal, and two-hop AWGN relay channels.