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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.
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