Signal-to-noise ratio performance limitations for input disturbance rejection in output feedback control

Communication channels impose a number of obstacles to feedback control. One recent line of research considers the problem of feedback stabilization subject to a constraint on the channel signal-to-noise ratio (SNR). We use the spectral factorization induced by the optimal solution and quantify in closed-form the infimal SNR required for both stabilization and input disturbance rejection for a minimum phase plant with relative degree one and memoryless additive white Gaussian noise (AWGN) channel. Finally we conclude by presenting a closed-form expression of the difference between the infimal AWGN channel capacity for input disturbance rejection and the infimal AWGN channel capacity required only for stabilizability.