## 2009.26: Structured Polynomial Eigenproblems Related to Time-Delay Systems

2009.26:
H. Fassbender, D. S. Mackey, N. Mackey and C. Schroder
(2009)
*Structured Polynomial Eigenproblems Related to Time-Delay Systems.*

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## Abstract

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 that compares favorably with the QZ algorithm is presented along with numerical experiments

Item Type: | MIMS Preprint |
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Uncontrolled 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 systems, delay-differential equations, stability analysis. |

Subjects: | MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 34 Ordinary differential equations MSC 2000 > 47 Operator theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2009.26 |

Deposited By: | Ms Lucy van Russelt |

Deposited On: | 26 March 2009 |

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