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

Authors:
Kunihisa Okano;Shinji Hara;Hideaki Ishii
Affiliations:
Department of Information Physics and Computing, The University of Tokyo, Tokyo 113-8656, Japan;Department of Information Physics and Computing, The University of Tokyo, Tokyo 113-8656, Japan;Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 226-8502, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

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 relationship between the mutual information of control signals and the unstable zeros of the open-loop transfer function.