Disturbance Rejection with Information Constraints: Performance Limitations of a Scalar System for Bounded and Gaussian Disturbances

We deal with disturbance rejection of a scalar system and show a unified derivation of the performance limitations for bounded and Gaussian disturbances under corresponding information constraints. The derivation is based on the common properties of two kinds of entropies. The limitations are described as the quantitative trade-offs between available amount of information and achievable control performances. We see that the limitations under communication constraints can be derived from the fact that the information constraints are weaker than the communication constraints, but the limitations under the information constraints can be achieved by the optimal coding system under the communication constraints.