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Inner–outer factorization for differential-algebraic systems

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Universität Hamburg, Fachbereich Mathematik, Bundesstraße 55 (Geomatikum), 20146, Hamburg, Germany

    Timo Reis

  2. Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623, Berlin, Germany

    Matthias Voigt

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  1. Timo Reis
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  2. Matthias Voigt
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Correspondence to Timo Reis.

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This work was supported by the International Max Planck Research School for Advanced Methods in Process and Systems Engineering and in the framework of the Einstein Center for Mathematics (ECMath) supported by the Einstein Foundation Berlin

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Reis, T., Voigt, M. Inner–outer factorization for differential-algebraic systems. Math. Control Signals Syst. 30, 15 (2018). https://doi.org/10.1007/s00498-018-0221-5

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