Sensitivity Analysis of Continuous-Time Linear Control Systems subject to Control and Measurement Noise: An Information-Theoretic Approach

Abstract: Sensitivity of linear continuous-time control 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 control trade-offs. When the signals of the control system are stationary Gaussian, these four different Bode-like integrals can be represented as 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.