A framework for linear control over channels with signal-to-noise ratio constraints

We present a framework for the solution of control and estimation problems under a signal-to-noise (SNR) ratio constraint. The framework can be used to design optimal linear controllers, based on output feedback, with two degrees of freedom: One part of the controller is placed before the communication channel and represents sensing and encoding operations. The other part represents decoding and issuing of the control signal. The framework includes a generalized plant model that can be used to represent problem instances covered in previous papers [12], [11] as special cases. It is shown that the design problem can be solved by minimization of a convex functional depending on the 1- and 2-norms of the Youla parameter, followed by a spectral factorization.