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Inner–outer factorization for differential-algebraic systems

  • Timo Reis
  • Matthias Voigt
Original Article
  • 41 Downloads

Abstract

We consider transfer functions of linear time-invariant differential-algebraic systems. Based on the stabilizing solutions of certain differential-algebraic Lur’e equations, we will derive simple formulas for realizations of inner–outer factorizations. We show that the existence of a stabilizing solution only requires behavioral stabilizability of the system. We neither assume properness nor (proper) invertibility of the transfer function. We briefly discuss numerical aspects for the determination of such factorizations.

Keywords

Differential-algebraic systems Inner–outer factorizations Lur’e equations Riccati equations 

Notes

Acknowledgements

The authors thank Olaf Rendel for the support in dealing with the numerical examples.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universität Hamburg, Fachbereich MathematikHamburgGermany
  2. 2.Technische Universität Berlin, Institut für MathematikBerlinGermany

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