Logarithmic integrals and system dynamics: An analogue of Bode's sensitivity integral for continuous-time, time-varying systems

A new time-domain interpretation of Bode's integral is presented. This allows for a generalization to the class of time-varying systems which possess an exponential dichotomy. It is shown that the sensitivity function is constrained, on average, by the spectral values in the dichotomy spectrum of the antistable component of the open-loop dynamics.

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