Sensitivity analysis of linear continuous-time feedback systems subject to control and measurement noise: An information-theoretic approach

Sensitivity of linear continuous-time SISO feedback systems, subject to control and measurement noise, is analyzed by deriving the lower bounds of Bode-like integrals via an information-theoretic approach. Bode integrals of four different sensitivity-like functions are employed to gauge the performance limitations of feedback systems. When the signals of the control system are stationary Gaussian, these four different Bode-like integrals can be represented as the differences between mutual information rates. These mutual information rates and hence the corresponding Bode-like integrals are proven to be bounded below by the unstable poles and zeros of the plant model, if the signals of the control system are wide-sense stationary.