Information theoretic limit and bound of disturbance rejection in LTI systems: Shannon entropy and H∞ entropy

By investigating the transmission of information and uncertainty in multivariable LTI systems disturbed by stationary random processes, the present paper discussed the connections within information rates, Bode integral and H_∞ entropy. For the regulation problem, performance limits of disturbance rejection are formulated in the framework of information theory, by connecting entropy rate to Bode integral formula. The "conservation law of variety" is revised. For the tracking problem, an upper bound of disturbance rejection performance is derived based on a proved relation between information rates and H_∞ entropy. The present results demonstrate that information rates are useful in control system analysis.