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A Condensed Form for Nonlinear Differential-Algebraic Equations in Circuit Theory

In: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

Author

Listed:
  • Timo Reis

    (University of Hamburg, Department of Mathematics)

  • Tatjana Stykel

    (Universität Augsburg, Institut für Mathematik)

Abstract

We consider nonlinear differential-algebraic equations arising in modelling of electrical circuits using modified nodal analysis and modified loop analysis. A condensed form for such equations under the action of a constant block diagonal transformation will be derived. This form gives rise to an extraction of over- and underdetermined parts and an index analysis by means of the circuit topology. Furthermore, for linear circuits, we construct index-reduced models which preserve the structure of the circuit equations.

Suggested Citation

  • Timo Reis & Tatjana Stykel, 2015. "A Condensed Form for Nonlinear Differential-Algebraic Equations in Circuit Theory," Springer Books, in: Peter Benner & Matthias Bollhöfer & Daniel Kressner & Christian Mehl & Tatjana Stykel (ed.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, edition 127, chapter 0, pages 503-531, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-15260-8_18
    DOI: 10.1007/978-3-319-15260-8_18
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