H∞ -: Optimal control of multi-rate sampled-data systems

The hybrid MRSD (multi-rate sampled-data) system is considered which consist of a continuous time plant and a digital lifted controller. This paper describes an explicit solution to the multi-rate H-infinity-optimal control problem using Nehari's theorem. The solution is based on lifting method, where an equivalent LTI system is obtained for the given periodic multi-rate problem. The causality constraint on the controller structure in lifting based solutions is automatically satisfied. By solving a standard Nehari's problem, we get the optimal parameterization of linear stabilizing controller in worst case l(2) to l(2) sense and hence the optimal h-periodic controller for the multirate systems.