Optimal H∞ control of hybrid multirate systems

The problem of using a synchronous multirate digital controller for a continuous-time plant is considered. The performance objective considered is the H^∞ norm of the periodically time-varying continuous-time input-output behavior of the closed-loop system. A continuous-time lifting technique is used to solve this hybrid sampled-data problem. This approach yields an equivalent purely discrete-time problem while preserving the multirate causality of the system. The latter problem can then be solved using known techniques