On the stability properties of polynomials with perturbed coefficients

Given a polynomial P_{c}(S) = S^{n} + t_{1}S^{n-1} + ... t_{n} = 0 which is Hurwitz or P_{d}(Z) = Z^{n} + t_{1}Z^{n-1} + ... t_{n} = 0 which has zeros only within or on the unit circle, it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1985-10, Vol.30 (10), p.1033-1036
Main Authors: Soh, C., Berger, C., Dabke, K.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Computer science
control theory
systems
Control system analysis
Control systems
Control theory. Systems
Differential equations
Exact sciences and technology
Large-scale systems
Linear systems
Mathematical model
Polynomials
Stability
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Summary:Given a polynomial P_{c}(S) = S^{n} + t_{1}S^{n-1} + ... t_{n} = 0 which is Hurwitz or P_{d}(Z) = Z^{n} + t_{1}Z^{n-1} + ... t_{n} = 0 which has zeros only within or on the unit circle, it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties. In this note, a method is presented for obtaining the largest hypersphere centered at t^{T} = [t_{1} ... t_{n}] containing only polynomials which are stable.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.1985.1103807