System structure and structural index

In the case of descriptor systems, phenomena can occur that are in principle not possible for state-space representations. For example, under certain circumstances, small perturbations at the input can cause arbitrarily large errors in the solution. A quantity that qualitatively describes significant problems of the concrete descriptor system is the index. On closer inspection, the index is only one quantity among various structural indices which, in the case of linear time-invariant systems, can be described by the Weierstrass or Kronecker normal form. These normal forms can be understood as generalizations of the Jordan normal form for matrices to regular and singular matrix pencils.

Publications

  • Röbenack, K.; Bausch, T.; Uhlig, A.: Struktureller Index von Deskriptorvariablen.
    In: Simulationstechnik, 15. Symposium in Paderborn, ASIM 2001, pp. 569-574
  • Reinschke, K. J.; Röbenack, K.: Graph-theoretic characterization of structural controllability for singular differential-algebraic equations.
    Presentation at the Annual GAMM Meeting 1999, Metz.
  • Röbenack, K.; Reinschke, K. J.: Digraph based determination of Jordan block size structure of singular matrix pencils.
    Linear Algebra and its Applications, 1998, 275-276, pp. 495-507.
  • Reinschke, K. J.; Röbenack, K.: Graph-theoretic determined Jordan-block-size structure of regular matrix pencils.
    Linear Algebra and its Applications, 1997, 263, pp. 333-348.
  • Reinschke, K. J.; Röbenack, K.; Wiedemann, G.: Strukturelle Analyse von Deskriptorsystemen mit Hilfe von Digraphen.
    Automatisierungstechnik - at, 1998, 46(1), S. 22-31.
  • Reinschke, K. J.; Röbenack, K: Graphentheoretische Bestimmung des strukturellen Index von Algebro-Differential-Gleichungssystemen für die Netzwerkanalyse.
    In: Mathis, W.; Noll, P. (Hrsg.): Neue Anwendungen theoretischer Konzepte in der Elektrotechnik mit Gedenksitzung zum 50. Todestag von Wilhelm Cauer, VDE-Verlag, 1996, S. 207-214. Tagungsband der 2. ITG-Diskussionssitzung, Berlin, 21. und 22. April 1995.