Optimal H-infinity design of causal multirate controllers and filters

Multirate sampled data systems employ more than one sampling frequency. Three main representations of such systems are presented: lifted representation, polyphase representation and frequency response matrix of a multirate system. All of these are used in the design and analysis of multirate controllers.;A two-stage design methodology is presented for the design of Hinfinity optimal multirate controllers. The first stage comprises a fast rate Hinfinity optimal controller design and its decomposition. The second stage involves lifting and a second optimal design in slow rate. The design methodology is used two design examples to obtain either a SISO or a MIMO multirate Hinfinity optimal controller. The proposed approach lead to multirate controllers that well approximate the Hinfinity closed-loop performance of an optimal fast rate design at an overall computational load similar to multirate controllers designed by resampling the low frequency part of the fast rate controller.;An algorithm for the design of multirate causal Hinfinity optimal controllers is presented. The controller design is based on the Youla parametrization of all stabilizing controllers. The causality of the controllers is assured by imposing constraints on the feedthrough term of its state space representation and the design problem is transformed into a constrained optimization problem, which is solved with the ellipsoid algorithm. The algorithm is validated through a controller design example.;The design of filter-banks is also studied. A lifting based design approach is proposed for the design of analysis and synthesis filter banks. The proposed methodology transforms the problem into a General Distance Problem where the filter bank designed is constrained to be causal. An iterative algorithm is also proposed to perform analysis and synthesis in the same design process. The results are validated with three filter-bank designs, which show small reconstruction error and same or better performance with lower filter complexity than some current design approaches.