Characterization of a complementary sensitivity property in feedback control: An information theoretic approach

This paper addresses a characterization of a complementary sensitivity property in feedback control using an information theoretic approach. We derive an integral-type constraint of the complementary sensitivity function with respect to the unstable zeros of the open-loop transfer function. It is an analogue of Bode’s integral formula for the sensitivity gain. To show the constraint, we first present a conservation law of the entropy and mutual information of signals in the feedback system. Then, we clarify the relation between the mutual information of a control signal and the unstable zeros of the open-loop transfer function.