New Versions of the Hermite Bieler Theorem in Stability Contexts

Zahreddine, Ziad

doi:10.11648/j.ajam.20190701.11

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Cited by 6 publications

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“…For more references in this context, see (Barnett, 1995), (Zahreddine, 2003), (Zahreddine, 2018), and (Zahreddine, 2019).…”

Section: Introductionmentioning

confidence: 99%

Order-Independent Algorithm for the Asymptotic Stability of Complex Polynomials

Zahreddine¹

2021

JMR

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The Extended Routh Array (ERA) settles the asymptotic stability of complex polynomials. The ERA is a natural extension of the Routh Array which applies only to real polynomials. Although the ERA is a nice theoretical algorithm for stability testing, it has its limitations. Unfortunately, as the order of the polynomial increases, the size of calculations increases dramatically as will be shown below. In the current work, we offer an alternative algorithm which is basically equivalent to the ERA, but has the extra advantage of being simpler, more efficient, and easy to apply even to large order polynomials. In all the steps required in the construction of the new algorithm, only one single and simple algebraic operation is needed, which makes it a polynomial order-independent algorithm.

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“…For more references in this context, see (Barnett, 1995), (Zahreddine, 2003), (Zahreddine, 2018), and (Zahreddine, 2019).…”

Section: Introductionmentioning

confidence: 99%