Model reduction of interconnected linear systems

Abstract

The problem of model reduction of linear systems with certain interconnection structure is considered in this paper. To preserve the interconnection structure between subsystems in the reduction, special care needs to be taken. This problem is important and timely because of the recent focus on complex networked systems in control engineering. Two different model reduction methods are introduced and compared in this paper. Both methods are extensions to the well-known balanced truncation method. Compared with earlier work in the area these methods use a more general linear fractional transformation framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that reduce to classical bounds in special cases are derived. The so-called structured Hankel singular values are used in the methods, and indicate how important states in the subsystems are with respect to a chosen input-output map for the entire interconnected system. It is shown how these structured Hankel singular values can be used to select an approximation order. Finally, the two methods are applied to a model of a mechanical device.

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