K-L information rate and H∞ entropy in linear control systems

Kullback-Leibler (K-L) information rate was used to measure the performance of linear control system with stationary stochastic disturbance and measurement noise. The K-L performance function was proved to be connected with the system H_∞ entropy, which is an auxiliary design criterion adopted in the field of H_∞ control. Based on this connection and a certain property of the H_∞ entropy, a relation between the K-L performance of the system with extraneous noise input and the H₂ performance of system with parameter perturbation was formulated.