H∞ control for discrete-time systems with multiple preview channels

The paper considers the discrete-time H_∞ control problem for systems involving multiple preview disturbance channels. A necessary and sufficient condition under which the problem is solvable is established. The condition and a desired H_∞ controller are given based on the solutions of a variant structure H_∞ Riccati equation and an H_∞-like Riccati equation. Both the Riccati equations admit a solution under a smaller level of disturbance attenuation than that required for the existence of a stabilizing solution to the standard H_∞ Riccati equation and their dimensions are independent of the preview length and the number of the disturbance input channels. Different from the pure single H_∞ preview control problem, we introduce variant structure disturbances, which is the key for our analysis in the paper.