H∞-optimal control of multi-rate sampled-data systems

The hybrid multi-rate sampled-data system is considered which consist of a continuous time plant and a digital lifted controller. The paper describes an explicit solution to the multi-rate H_∞-optimal control problem using Nehari´s theorem. The solution is based on a 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 problem, we obtain the optimal parameterization of a linear stabilizing controller in a worst case l₂ to l₂ sense and hence the optimal h-periodic controller for the multirate systems.