Extended optimality properties of the linear quadratic regulator and stationary Kalman filter

Results are presented showing that the constant-gain state-feedback solution to the infinite-time linear quadratic regulator problem is optimal not only for arbitrary initial conditions or white noise disturbances, but also for worst case L¹ disturbances. Similarly, in the stationary Kalman filter, the white disturbance and measurement noise can be replaced by unknown bounded energy signals, and optimality still holds if the performance criterion is a time-domain L^∞ norm of the state estimation errors in the presence of worst case energy signals