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., dn > dn-1 > > d1 > d0 > 0. In this letter it is shown that even if the monotonic condition is violated by one coefficient (say dk), D(z) is still Schur stable if the deviation of dk from dk+1 or dk-1 is not too large. More precisely we derive upper bounds for the admissible deviations of dk from dk+1 or dk-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 dk than an existing result.