Discrete time H∞ preview control

The paper discusses the H_∞ preview control problem. We apply simple tools such as completion of square to solve the problem. The sufficient and necessary condition under which the finite-horizon problem is solvable is provided and is actually the inertia condition reflecting the aftereffect from the disturbance. Different from existing results, the proposed controller is given by a Riccati equation with the same dimension as the original state, which is similar to that of the standard H_∞ control. Both the finite horizon and infinite horizon cases are considered. The idea can be extended to systems with multiple-channel preview.