IEICE Trans - On the Monotonic Condition for Schur Stability of Real Polynomials

On the Monotonic Condition for Schur Stability of Real Polynomials

Younseok CHOO
Gin-Kyu CHOI

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E94-A No.12 pp.2886-2888
Publication Date: 2011/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E94.A.2886
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Systems and Control
Keyword:
real polynomial, Schur stability, monotonic condition, dominant condition,

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Summary:
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.