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Journal of Dynamics and Differential Equations

, Volume 26, Issue 4, pp 889–914 | Cite as

Analysis of Linear Variable Coefficient Delay Differential-Algebraic Equations

  • Phi Ha
  • Volker MehrmannEmail author
  • Andreas Steinbrecher
Article

Abstract

The analysis of general linear variable coefficient delay differential-algebraic systems (DDAEs) is presented. The solvability for DDAEs is investigated and a reformulation procedure to regularize a given DDAE is developed. Based on this regularization procedure existence and uniqueness of solutions and consistency of initial functions is analyzed as well as other structural properties of DDAEs like smoothness requirements. We also present some examples to demonstrate that for the numerical solution of a DDAE, a reformulation of the system before applying numerical methods is essential.

Keywords

Differential-algebraic equation Delay differential-algebraic equation Regularization Existence of solutions Uniqueness of solutions Consistency conditions 

Mathematics Subject Classification

34A09 34A12 65L05 65H10 

Notes

Acknowledgments

We thank Vinh Tho Ma for carrying the numerical simulations in Examples 5.1 and 5.2. Phi Ha has been supported by Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 910 Control of self-organizing nonlinear systems: Theoretical methods and application concepts. V. Mehrmann and A. Steinbrecher has been supported by European Research Council through Advanced Grant MODSIMCONMP.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut für Mathematik, MA 4-5, TU BerlinBerlinGermany

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