Limitations of disturbance rejection in feedback systems with finite bandwidth

This paper studies limitations of disturbance rejection in closed-loop cont rol systems. The disturbance is modeled as colored noise, and disturbance r ejection is measured by the output variance. Lower bounds on the achievable output variance are derived under several practical constraints, the main one being a bound on the system bandwidth; constraints on the stability rob ustness (measured by the distance from the Nyquist plot to the critical poi nt) and the ability to track low-frequency reference signals (measured by t he sensitivity reduction at low frequencies) are also considered. The bound s are derived by finding the sensitivity function that minimizes the output variance. This optimization is performed subject to the above constraints and, in addition, subject to certain sensitivity integral constraints that arise because of closed-loop stability. The utility of the results is illus trated by analyzing the achievable level of passenger comfort in an aircraf t subjected to turbulence.