Bode integrals and laws of variety in linear control systems

Performance limits and deconstraints of linear feedback control systems disturbed by random noise are studied from the viewpoint of information theory. By using Bode integral formulas, information transmission in such systems is connected to unstable poles and nonminimum phase zeros of open-loop transfer functions. Performance limits of disturbance rejection are discussed by using such connection, and the conservation law of variety is revised based on a new extended definition of variety. Meanwhile, a necessary information condition which implies a new kind of design constraints of linear tracking problem is proposed with the concept of mutual information rate, and the law of requisite variety is derived from this condition.