Linear quadratic performance with worst case disturbance rejection

The method of the calculus of variations and the maximum principle are prep osed for the design of `LQR' controllers with the worst case disturbance re jection for a linear time-varying (LTV) plant on finite horizon. The distur bance is bounded by either the windowed L-2-norm or the windowed L-infinity -norm, or both. In the case of the windowed L-2-normed disturbance, uncerta in but norm bounded initial condition is also considered. Certain necessary and sufficient condtions for the existence of a linear controller are deri ved with the proof of the solution existence and uniqueness. The results ar e extended to the steady state ones for the linear time-invariant (LTIV) pl ant on the infinite horizon. A comparison to H-infinity control with transi ents is also presented. In the case of the windowed L-infinity-normed or bo th normed disturbances, the solution for the worst case disturbance is of s witching (or bang-bang) type.