H∞H∞ optimal terminal control for linear systems with delayed states and controls

In this paper we consider a linear time-varying system with state and control delay terms, both lumped and distributed, subject to unknown, square integrable disturbances. Using a differential games approach, we provide a necessary and sufficient condition for the existence of an optimal control law minimizing the H∞H∞ norm of the operator mapping the disturbance to the weighted control and terminal state.