Optimal constant controllers for stochastic linear systems

The design of a fixed, linear, dynamic controller for a linear system subjected to random disturbances and additive measurement noise is examined. The objective is to achieve satisfactory performance with controllers of order significantly lower than that of a Kalman filter or Luenberger observer. Matrices which define the controller are chosen to minimize the steady-state average of a quadratic function of the control and state variables. Necessary conditions which the gains must satisfy in order to minimize this criterion are developed.