Information Theoretic Interpretations for H-infinity Entropy

Based on the studies on information transmission in discrete multivariable linear time invariant (LTI) system disturbed by stationary noise, relations within entropy rate, mutual information rate and H-infinity entropy are discussed. For the general control systems, equivalent relations between entropy rate and H-infinity entropy are formulated by using spectral factorization. For the classic tracking systems, performance of disturbance rejection is measured by a difference of entropy rates (or mutual information rate in Gaussian case). This performance function is proved to be bounded by the H-infinity entropy of the closed-loop transfer function from disturbance to output. These relations give information theoretic interpretations for the minimum entropy H-infinity control theory. Potential application of these relations is discussed.