Linear Stochastic Control with a Reduced Order Filter

Abstract

Several aspects of an optimal regulator problem are discussed in this paper for linear stochastic systems with incomplete observation. First the explicit form of the reduced order controller is presented. It is also shown that the reduced order state estimator coincides with the controller obtained when the covariance matrix of the observation noise in a Kalman filter is brought to null. Second the practical stability criteria are established for the closed loop system resulted from interconnecting the plant and the controller. Since the stability depends only on zeros of the open loop transfer function, the additional condition is that it has a minimum phase shift. Finally, from the stability analysis, the conditions for the maximum accuracy to be achieved are directly derived.