ON STABILITY OF A POLYNOMIAL
- Resource Type
- Article
- Authors
- 김정헌; Wei Su; 송윤정
- Source
- Journal of Applied Mathematics and Informatics, 36(3), pp.231-236 May, 2018
- Subject
- 수학
- Language
- English
- ISSN
- 2234-8417
1598-5857
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.