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Mathematics of Control, Signals and Systems

, Volume 14, Issue 3, pp 233–256 | Cite as

Analysis of Over- and Underdetermined Nonlinear Differential-Algebraic Systems with Application to Nonlinear Control Problems

  • Peter Kunkel
  • Volker Mehrmann

Abstract.

 We study over- and underdetermined systems of nonlinear differential-algebraic equations. Such equations arise in many applications in circuit and multibody system simulation, in particular when automatic model generation is used, or in the analysis and solution of control problems in the behavior framework.¶We give a general (local) existence and uniqueness theory and apply the results to analyze when nonlinear implicit control problems can be made regular by state or output feedback.¶The theoretical analysis also leads immediately to numerical methods for the simulation as well as the construction of regularizing feedbacks.

Key words. Nonlinear differential-algebraic equations, Nonlinear control problems, Solvability, Model consistency, Behavior approach, Strangeness index, Regularization, Feedback design. 

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Copyright information

© Springer-Verlag London Limited 2001

Authors and Affiliations

  • Peter Kunkel
    • 1
  • Volker Mehrmann
    • 2
  1. 1.Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany.DE
  2. 2.FB 3 Mathematik, MA 4-5, Technische Universität Berlin, D-10623 Berlin, Germany.DE

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