On the Monotonic Condition for Schur Stability of Real Polynomials

Younseok CHOO; Gin-Kyu CHOI

doi:10.1587/transfun.E94.A.2886

On the Monotonic Condition for Schur Stability of Real Polynomials

Younseok CHOO, Gin-Kyu CHOI

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It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., d_n > d_n-1 > > d₁ > d₀ > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say d_k), D(z) is still Schur stable if the deviation of d_k from d_k+1 or d_k-1 is not too large. More precisely we derive upper bounds for the admissible deviations of d_k from d_k+1 or d_k-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for d_k than an existing result.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.12 pp.2886-2888

Publication Date: 2011/12/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E94.A.2886

Type of Manuscript: LETTER

Category: Systems and Control

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Younseok CHOO, Gin-Kyu CHOI, "On the Monotonic Condition for Schur Stability of Real Polynomials" in IEICE TRANSACTIONS on Fundamentals, vol. E94-A, no. 12, pp. 2886-2888, December 2011, doi: 10.1587/transfun.E94.A.2886.
Abstract: It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., d_n > d_n-1 > > d₁ > d₀ > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say d_k), D(z) is still Schur stable if the deviation of d_k from d_k+1 or d_k-1 is not too large. More precisely we derive upper bounds for the admissible deviations of d_k from d_k+1 or d_k-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for d_k than an existing result.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.2886/_p

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@ARTICLE{e94-a_12_2886,
author={Younseok CHOO, Gin-Kyu CHOI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Monotonic Condition for Schur Stability of Real Polynomials},
year={2011},
volume={E94-A},
number={12},
pages={2886-2888},
abstract={It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., d_n > d_n-1 > > d₁ > d₀ > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say d_k), D(z) is still Schur stable if the deviation of d_k from d_k+1 or d_k-1 is not too large. More precisely we derive upper bounds for the admissible deviations of d_k from d_k+1 or d_k-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for d_k than an existing result.},
keywords={},
doi={10.1587/transfun.E94.A.2886},
ISSN={1745-1337},
month={December},}

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TY - JOUR
TI - On the Monotonic Condition for Schur Stability of Real Polynomials
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2886
EP - 2888
AU - Younseok CHOO
AU - Gin-Kyu CHOI
PY - 2011
DO - 10.1587/transfun.E94.A.2886
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2011
AB - It is well known that an nth-order real polynomial D(z)= is Schur stable if its coefficients satisfy the monotonic condition, i.e., d_n > d_n-1 > > d₁ > d₀ > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say d_k), D(z) is still Schur stable if the deviation of d_k from d_k+1 or d_k-1 is not too large. More precisely we derive upper bounds for the admissible deviations of d_k from d_k+1 or d_k-1 to ensure the Schur stability of D(z). It is also shown that the results obtained in this letter always yield the larger stability range for d_k than an existing result.
ER -