A Nonlinear Version of Bode’s Sensitivity Integral: Connections with Entropy and Nonlinear Inner-outer Factorizations

For linear systems, we show that the constraint known as Bode’s sensitivity integral has an information theoretic interpretation in terms of the difference in the entropy rates between the input and output of the systems. We use this interpretation to show that, if the open loop system is globally exponentially stable, this difference is zero. For nonlinear systems that are not stable, we start to investigate the method to calculate this difference using new results on the inner/outer factorization of nonlinear systems.