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

It is shown that the constant gain state-feedback solution to the infinite-time linear quadratic regulator problem is optimal not only for arbitrarily initial conditions or white noise disturbances, but also for worst-case L¹ disturbances. Using a similar technique, it is shown that in the stationary Kalman filter, the white disturbance and measurement noise can be replaced by unknown bounded energy signals, and that optimality still holds if the performance criterion is a time domain L_∞ normal of the state estimation errors in the presence of worst-case energy signals