Optimal Linear Control for Channels with Signal-to-Noise Ratio Constraints

We consider the problem of stabilizing and minimizing the disturbance response of a SISO LTI plant, subject to a stochastic disturbance, over an analog communication channel with additive white noise and a signal-to-noise ratio (SNR) constraint. The controller is linear, based on output feedback and has a structure with two degrees of freedom: One part represents sensing and encoding operations and the other part represents decoding and issuing the control signal. It is shown that the problem of simultaneously designing the two optimal controller parts can be solved in two stages: First a functional depending both on the 1- and 2-norms of the Youla parameter is minimized. This minimization can be arbitrarily well approximated by a quasiconvex program. The second stage consists of a spectral factorization.