Disturbance rejection with information constraints: Performance limitations of a scalar system for bounded and Gaussian disturbances

This paper derives performance limitations for disturbance rejection of scalar systems under information constraints subject to either bounded or Gaussian disturbances. Two kinds of disturbance are treated in a unified manner, using appropriate entropies and distortions. It is shown that the achievable performance cannot be improved even if the maximum information constraint is relaxed to an average information constraint. Another observation is that, while the information constraints are weaker than bit-rate or signal-to-noise ratio constraints on the communication channel, the same performance levels are achieved by the best encoder and decoder for disturbance rejection with the information constraints.