Model reduction of interconnected systems

Large scale linear systems are often composed of subsystems that interconnect to each other. Instead of reducing the entire system without taking into account its structure, it makes sense to reduce each subsystem (or a few of them) by taking into account its interconnection with the others subsystems in order to approximate the entire system. This is the purpose of this paper. Interconnected (or aggregated) systems have been studied in the eighties [1] in the model reduction framework, but received recently only little attention [2]. It turns out that many model reduction techniques such as weighted balanced truncation, controller reduction and second-order balanced truncation can be seen as particular interconnected model reduction techniques. Let us assume that we are given a large scale linear system G(s). This system is composed of an interconnection of k sub-systems Ti(s). Each subsystem is assumed to be a linear MIMO transfer function. Subsystem Tj(s) has αj inputs denoted by the vector aj and βj outputs denoted by the vector bj : bi(s) = Ti(s)ai(s). (1)