Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON STABILITY OF A POLYNOMIAL

  • KIM, JEONG-HEON (Department of Mathematics, Soongsil University) ;
  • SU, WEI (Department of Mathematics, Soongsil University) ;
  • SONG, YOON J. (Department of Mathematics, Soongsil University)
  • Received : 2017.11.01
  • Accepted : 2018.02.13
  • Published : 2018.05.30
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Abstract

A polynomial, $p(z)=a_0z^n+a_1z^{n-1}+{\cdots}+a_{n-1}z+a_n$, with real coefficients is called a stable or a Hurwitz polynomial if all its zeros have negative real parts. We show that if a polynomial is a Hurwitz polynomial then so is the polynomial $q(z)=a_nz^n+a_{n-1}z^{n-1}+{\cdots}+a_1z+a_0$ (with coefficients in reversed order). As consequences, we give simple ratio checking inequalities that would determine unstability of a polynomial of degree 5 or more and extend conditions to get some previously known results.

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References

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