The Location of the Zeros of the Derivative of a Polynomial

Marden, Morris

doi:10.1080/00029890.1935.11987717

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…The proof of Lemma 4 follows the same lines as the proof of Theorem 7.2 from Reference 10. It relies on properties of self‐inversive polynomials, the standard A. Cohn Theorem 16 and the one due to Eneström‐Kakeya 17,18 ; see also References 19–22 for further insights on polynomials with all zeros on the unit circle.…”

Section: On Delay Difference Equations With Two Interfering Delays An...mentioning

confidence: 99%

Prescribing transport equation solution's decay via multiplicity manifold and autoregressive boundary control

Ammari,

Boussaada,

Niculescu

et al. 2024

Intl J Robust & Nonlinear

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This article addresses the boundary control problem of the transport equation. Namely, we propose a control method, which is merely a delayed output feedback relying on a partial pole placement idea, that consists in assigning an appropriate exponential decay rate to the closed‐loop system's solution. The proposed control structure appearing in the transport boundary, which has proven its effectiveness in controlling finite dimensional systems, consists of an autoregressive relation linking the transport equation's input and output. The obtained result provides an analytical lower bound for the solution's exponential decay. The contribution is concluded with a numeric discussion on the concrete implementation of the method with a special emphasis on the delay seen as a control parameter.

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Section: On Delay Difference Equations With Two Interfering Delays An...mentioning

confidence: 99%

Prescribing transport equation solution's decay via multiplicity manifold and autoregressive boundary control

Ammari,

Boussaada,

Niculescu

et al. 2024

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…For a historic account on the Lucas theorem see [6,Section 2]. For applications of the Lucas theorem in different settings see [1,4,7,8,9,10,11,13].…”

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confidence: 99%