Low-sensitivity feedback controllers for linear systems with incomplete state information

Abstract

Abstract The problem of output feedback controller design with low trajectory sensitivity to small system parameter variations is considered for both deterministic and stochastic systems. The performance index is of the standard linear regulator type modified to include a quadratic sensitivity term. A concise derivation of the necessary conditions for optimality is presented for deterministic systems using the method of Lagrange multipliers and existence of an optimal solution is proven. The low sensitivity controller is realized by a gain matrix obtained from the solution of a set of non-linear matrix equations. Also, use is made of recent observer-estimator results to present a unified approach to low-sensitivity controller design for stochastic systems.