Periodic two-dimensional descriptor systems
(2023) The Electronic Journal of Linear Algebra — Vol. 39, p. 472-490 (2023)
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- Authors
Benner, Peter 
Van Dooren, Paul
- Abstract
- In this note, we analyze the compatibility conditions of 2D descriptor systems with periodic coefficients and we derive a special coordinate system in which these conditions reduce to simple matrix commutativity conditions. We also show that the compatibility of the different trajectories in such a periodic 2D descriptor system can elegantly be formulated in terms of so-called matrix relations of regular pencils, which were introduced in [Benner and Byers. An arithmetic for matrix pencils: Theory and new algorithms. Numer. Math., 103(4):539-573, 2006]. We then show that these ideas can be extended to multidimensional periodic descriptor systems and briefly discuss the difference between the case of complex and real coefficient matrices.
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Citations
Benner, P., & Van Dooren, P. (2023). Periodic two-dimensional descriptor systems. The Electronic Journal of Linear Algebra, 39, 472-490. https://doi.org/10.13001/ela.2023.7989 (Original work published 2023)