Two-stage design of multirate ℋ∞ optimal controllers

A new methodology is presented for the design of ℋ_∞ optimal multirate controllers. A key feature of the proposed approach is the design of the slow rate part of the multirate controller via lifting and ℋ_∞ optimization. This approach addresses potential problems of aliasing due to the multirate controller by taking into consideration closed-loop performance. Our results are illustrated by a design example and compared to the resampling approach in terms of frequency response measures and closed-loop time responses. The proposed design methodology leads to multirate controllers that well approximate the ℋ_∞ closed-loop performance of an optimal fast rate design at an overall computational cost similar to multirate controllers designed by resampling.