Robust Stability of Differential-Algebraic Equations

  • Nguyen Huu Du
  • Vu Hoang LinhEmail author
  • Volker Mehrmann
Part of the Differential-Algebraic Equations Forum book series (DAEF)


This paper presents a survey of recent results on the robust stability analysis and the distance to instability for linear time-invariant and time-varying differential-algebraic equations (DAEs). Different stability concepts such as exponential and asymptotic stability are studied and their robustness is analyzed under general as well as restricted sets of real or complex perturbations. Formulas for the distances are presented whenever these are available and the continuity of the distances in terms of the data is discussed. Some open problems and challenges are indicated.


Differential-algebraic equation Restricted perturbation Robust stability Stability radius Spectrum Index 

Mathematics Subject Classification

93B35 93D09 34A09 34D10 



V.H. Linh supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2011.14. V. Mehrmann supported by Deutsche Forschungsgemeinschaft, through project A02 within Collaborative Research Center 910 Control of self-organizing nonlinear systems.

We thank the anonymous referees for their useful suggestions that led to improvements of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nguyen Huu Du
    • 1
  • Vu Hoang Linh
    • 1
    Email author
  • Volker Mehrmann
    • 2
  1. 1.Faculty of Mathematics, Mechanics and InformaticsVietnam National UniversityHanoiVietnam
  2. 2.Institut für Mathematik, MA 4-5Technische Universität BerlinBerlinFed. Rep. Germany

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