Inner–outer factorization for differential-algebraic systems

  • Timo ReisEmail author
  • Matthias Voigt
Original Article


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.


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



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


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Authors and Affiliations

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

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