Stability of polynomials under coefficient perturbation

Author

Bialas, S. ; Garloff, J.

Author_Institution

Academy of Mining and Metallurgy, Crakow, Poland

Volume

Issue

fYear

1985

fDate

3/1/1985 12:00:00 AM

Firstpage

310

Lastpage

312

Abstract

Let the real polynomial $a_{0}x^{n} + a_{1}x^{n-1} + ... + a_{n-1}x + a_{n}$ be stable and let the real numbers $b_{k}, c_{k} \\geq 0, 0 \\leq k \\leq n$ , be given. We present a simple determinant criterion for finding the largest $t_{0} \\geq 0$ such that the polynomial $\\alpha _{0}x^{n} + \\alpha _{1}x^{n-1}+ ... +\\alpha _{n-1}x + \\alpha _{n}$ is stable for all $\\alpha _{k} \\in (a_{k} - b_{k}t_{0}, a_{k} + C_{k}t_{0}) cup {a_{k}}, 0 \\leq k \\leq n$ . Several further observations allow us to reduce the computational cost considerably.

Keywords

Perturbation methods; Polynomials; Stability; Convergence; Distributed parameter systems; Liquids; Optimal control; Partial differential equations; Polynomials; Stability; State estimation; Stochastic systems; Upper bound;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1985.1103930

Filename

1103930

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=848865