A Structured Model Reduction Method for Linear Interconnected Systems

This paper develops a model reduction method for a large-scale interconnected system that consists oflinear dynamic components. In the model reduction, we aim to preserve physical characteristics of each component. To this end, we formulate a structured model reduction problem that reduces the model order of components while preserving the feedback structure. Although there are a few conventional methods for such structured model reduction to preserve stability, they do not explicitly consider performance of the reduced-order feedback system. One of the difficulties in the problem with performance guarantee comes from nonlinearity of a feedback system to each component. The problem is essentially in a class of nonlinear optimization problems, and therefore it cannot be efficiently solved even in numerical computation. In this paper, application of an equivalent transformation and a proper approximation reduces this nonlinear problem to a problem of the weighted linear model reduction. Then, by using the weighted balanced truncation technique, we construct a reduced-order model with preserving the feedback structure to ensure small modeling error. Finally, we verify the effectiveness of the proposed method through numerical experiments.