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Preprint 32-2008

Passivity-preserving balanced truncation for electrical circuits

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Author(s) : Timo Reis , Tatjana Stykel

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 32-2008

MSC 2000

34A09 Implicit equations, differential-algebraic equations
15A24 Matrix equations and identities

Abstract :
We present a passivity-preserving balanced truncation model reduction method for differential-algebraic equations arising in circuit simulation. This method is based on balancing the solutions of projected Lur'e equations. By making use of the special structure of circuit equations, we can reduce the numerical effort for balanced truncation significantly. It is shown that the property of reciprocity is also preserved in the reduced-order model. Network topological interpretations of certain circuit effects are given. The presented theory is illustrated by a numerical example.

Keywords : balanced truncation, bounded real, electrical circuits, Lur'e equations, model reduction, passivity, positive real, projectors, reciprocity, Riccati equations

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