Geodesic
Structured polynomial eigenproblems related to time-delay systems
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 306-330
A new class of structured polynomial eigenproblems arising in the stability analysis of time-delay systems is identified and analyzed together with new types of closely related structured polynomials. Relationships between these polynomials are established via the Cayley transformation. Their spectral symmetries are revealed, and structure-preserving linearizations constructed. A structured Schur decomposition for the class of structured pencils associated with time-delay systems is derived, and an algorithm for its computation, which compares favorably with the QZ algorithm, is presented along with numerical experiments.
Classification : 15A18, 15A21, 15A22, 34K06, 34K20, 47A56, 47A75, 65F15
Keywords: polynomial eigenvalue problem, palindromic matrix polynomial, quadratic eigenvalue problem, even matrix polynomial, structure-preserving linearization, matrix pencil, structured Schur form, real QZ algorithm, spectral symmetry, Cayley transformation, involution, time-delay system, delay-differential equation, stability analysis 
@article{ETNA_2008__31__a4,
     author = {Fassbender,  Heike and Mackey,  D.Steven and Mackey,  Niloufer and Schr\"oder,  Christian},
     title = {Structured polynomial eigenproblems related to time-delay systems},
     journal = {Electronic transactions on numerical analysis},
     pages = {306--330},
     year = {2008},
     volume = {31},
     zbl = {1188.15007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a4/}
}
TY  - JOUR
AU  - Fassbender,  Heike
AU  - Mackey,  D.Steven
AU  - Mackey,  Niloufer
AU  - Schröder,  Christian
TI  - Structured polynomial eigenproblems related to time-delay systems
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 306
EP  - 330
VL  - 31
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__31__a4/
LA  - en
ID  - ETNA_2008__31__a4
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%0 Journal Article
%A Fassbender,  Heike
%A Mackey,  D.Steven
%A Mackey,  Niloufer
%A Schröder,  Christian
%T Structured polynomial eigenproblems related to time-delay systems
%J Electronic transactions on numerical analysis
%D 2008
%P 306-330
%V 31
%U http://geodesic.mathdoc.fr/item/ETNA_2008__31__a4/
%G en
%F ETNA_2008__31__a4
Fassbender,  Heike; Mackey,  D.Steven; Mackey,  Niloufer; Schröder,  Christian. Structured polynomial eigenproblems related to time-delay systems. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 306-330. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a4/