Structured model reduction of interconnected linear systems based on singular perturbation

Abstract

This paper proposes a singular perturbation approximation that preserves system passivity and an interconnection topology among subsystems. In the first half of this paper, we develop a singular perturbation approximation valid for stable linear systems. Using the relation between the singular perturbation and the reciprocal transformation, we derive a tractable expression of the error system in the Laplace domain, which provides a novel insight to regulate the approximating quality of reduced models. Then in the second half, we develop a structured singular perturbation approximation that focuses on a class of interconnected systems. This structured approximation provides a reduced model that not only possesses fine approximating quality, but also preserves the original interconnection topology and system passivity.