Controller Reduction with Combination of Generalized Gramians

Abstract

In this paper, a new controller reduction method using generalized Gramians (generalized controllability and observability Gramians) is proposed. In order to obtain the generalized Gramians which have block diagonal structure, a considering control system is described by using right and left coprime factorizations of the plant and the controller. For the system and its subsystems (sensitivity function etc.), H∞ error norms of the subsystems (the system) with a reduced-order controller yield an upper bound of H∞ performance of the system (each subsystem) with the reduced-order controller. From the viewpoint of the relation, the reduced-order controllers in the proposed method are obtained with combination of the structured generalized Gramians of the subsystems. Finally, several numerical examples are used to verify the availability of the proposed method.