(M, N)-approximation: a system simplification method

Abstract

A method is presented for the simplification of systems made up of N interacting 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. 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 that compares the new method with other existing balancing methods, and the results are shown to be in favour of the new method.