Logarithmic integrals and system dynamics: an analogue of Bodeʹs sensitivity integral for continuous-time, time-varying systems Original Research Article

A new time-domain interpretation of Bodeʹs 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.