Periodic descriptor systems: Solvability and conditionability

Sreedhar, J;Van Dooren, Paul
(1999) IEEE Transactions on Automatic Control — Vol. 44, n° 2, p. 310-313 (1999)

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  • Sreedhar, J
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  • Van Dooren, PaulUCLouvain
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Abstract
The authors consider discrete-time linear periodic descriptor systems and study the concepts of solvability and conditionability, introduced by Luenberger. They prove that solvability is equivalent to conditionability, just as in the time-invariant case. We give a characterization of solvability/conditionability in terms of a cyclic matrix: pencil and, furthermore, propose a simple test,ia the periodic Schur decomposition to check for either property. This could lead to further systematic study of these systems.
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Sreedhar, J., & Van Dooren, P. (1999). Periodic descriptor systems: Solvability and conditionability. IEEE Transactions on Automatic Control, 44(2), 310-313. https://doi.org/10.1109/9.746256 (Original work published 1999)