Optimal H^∞ and H² control of hybrid multirate systems

The problem of using a synchronous multirate digital controller for a continuous-time plant is considered. The performance objectives considered are the H^∞ and the H² norms of the periodically time-varying continuous-time input-output behavior of the closed loop system. A continuous-time lifting technique is used to solve these hybrid sampled-data problems. This approach yields equivalent purely discrete-time problems while preserving the multirate causality of the systems. The later problems can then be solved using known techniques.