H∞ control for systems with two classes of disturbances

The paper considers H∞ preview control problem for the systems simultaneous involving the unpreviewable disturbance. Due to the outer optimization is a control problem for the systems with multiple channels and a single delay, the problem is a nontrivial extension of the existed results. The paper aims to provide the necessary and sufficient condition under which the problem is solvable. The condition and the desired controller are based on an H∞-like Riccati equation with the same dimension as the system with a null delay, which plays a role as the H∞ Riccati equation in the standard H∞ control problem does. The idea can also be applied to solve H∞ problem for systems with multiple and different preview channels.