Preprint 25-2008

Positive real and bounded real balancing for model reduction of descriptor systems

Author(s) : Timo Reis , Tatjana Stykel

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 25-2008

MSC 2000

34A09 Implicit equations, differential-algebraic equations

93C05 Linear systems

Abstract :
We present an extension of the positive real and bounded real balanced truncation model reduction methods to large-scale descriptor systems. These methods are based on balancing the solutions of the projected Lur'e matrix equations. Important properties of these methods are that, respectively, passivity and contractivity are preserved in the reduced-order models and that there exist approximation error bounds. We also discuss the numerical solution of the projected Lur'e equations. Numerical examples are given.

Keywords : descriptor systems, passivity, contractivity, positive real, bounded real, model reduction, balanced truncation, Lur'e equations