Sensitivity Reduction by State Derivative Feedback

This paper shows that the sensitivity of state feedback control systems can be reduced by additional state derivative feedback, for a fixed closed loop eigenstructure. The price of this sensitivity reduction is in general noise response amplification. Two indices which quantify stability robustness and response sensitivity are given for time invariant continuous time and discrete time systems, together with an index of response to disturbances and noise. Closed form expressions for the gradients of these indices are given. A two step design procedure is proposed which consists of first selecting a closed loop eigenstructure, then minimizing one of the sensitivity indices under a magnitude constraint on the noise response. Examples are given to illustrate this original design procedure.