BIT Numerical Mathematics

, Volume 58, Issue 4, pp 1049–1077 | Cite as

Regular solutions of DAE hybrid systems and regularization techniques

  • Peter Kunkel
  • Volker Mehrmann


The solvability and regularity of hybrid differential-algebraic systems (DAEs) is studied, and classical stability estimates are extended to hybrid DAE systems. Different reasons for non-regularity are discussed and appropriate regularization techniques are presented. This includes a generalization of Filippov regularization in the case of so-called chattering. The results are illustrated by several numerical examples.


Differential-algebraic equation Hybrid system Switched system Index reduction Existence and uniqueness of solutions Filippov regularization Strangeness index Chattering 

Mathematics Subject Classification

34K34 34K28 65L80 65L05 34K32 


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität LeipzigLeipzigGermany
  2. 2.Institut für MathematikTechnische Universität BerlinBerlinGermany

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