MATHEMATICAL ENGINEERING TECHNICAL REPORTS 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 show 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 control signals and the unstable zeros of the open-loop transfer function.