Singular Descriptor Systems and Generalized Inverses

In the linear-time invariant case, singular descriptor systems are characterized by the fact that for them the matrix pencil $sE-A$ describing the system dynamics is not invertible (i.e., not regular, but singular). This is true, for example, of rectangular matrixschaars. If the classical inverse of the matrix pencil $sE-A$ does not exist, one can resort to various generalized inverses (Moore-Penrose inverse, Drazin inverse).

Example

• Drazin inverse
• Weak Drazin inverse

Publications

• Röbenack, K.; Reinschke, K. On generalized inverses of singular matrix pencils.
  Applied Mathematics and Computer Science, 2011, 21(1), pp. 161-172
• Röbenack, K.; Reinschke, K. J.: On the Index of Matrices and Singular Matrix Pencils.
  Presentation at the Annual GAMM Meeting 1999, Metz.
• Reinschke, K. & Röbenack, K.: Graphentheoretische Analyse des Eingangs-Ausgangsverhaltens singulärer Deskriptorsysteme.
  In: K. Gens, W. (Hrsg.), Tagungsband 42. Internationales Wissenschaftliches Kolloquium, Band 3, TU Ilmenau, 1997, 107-112