(M,N)-Approximation: A System Simplification Method

This paper presents a method for the simplification of systems made up of N interconnected subsystems, by approximating only M of the N subsystems. It is proposed to reduce each of the M subsystems while all interactions are active, and to preserve the identities of all subsystems in the overall approximation, as demanded in many situations. Problems of conventional model reduction, controller or compensator reduction, reduction of finite element models, reduction of decentralized controllers, etc., can be treated as specific applications of this method. In this preliminary paper, conventional model reduction methods, but constrained to meet the above objectives, are employed. As an application to controller reduction, a new version of balanced controllers is shown to be generated by this method. A numerical example is included which compares the new method with other existing balancing methods, and the results are shown to be in favor of the new method. Due to the page limitations, only a summary is included in the proceedings; a detailed version would be distributed at the presentation.