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Chapter 1 Stabilization and Control over Gaussian Networks

We provide an overview and some recent results on real-time communication and control over Gaussian channels. In particular, the problem of remote stabilization of linear systems driven by Gaussian noise over Gaussian relay channels is considered. Necessary and sufficient conditions for mean-square stabilization are presented, which reveal signal-to-noise ratio requirements for stabilization which are tight in certain class of settings. Optimal linear policies are constructed, global optimality and sub-optimality of such policies are investigated in a variety of settings. We also consider the design of low-delay sensing and transmit schemes for real-time communication. 1.