Analytic constraints in feedback control of linear time-varying systems: Bode's sensitivity integral

In this paper it is shown how Bode's integral has a natural generalization for time-varying systems which possess an exponential dichotomy. Moreover, the sensitivity function is constrained, on average, by the lower Bohl and Lyapunov exponents of the open-loop system. These take the place of the magnitude of the open-loop poles. The analysis is carried out for discrete-time systems.