scholarly journals Matrix-valued Hermitian Positivstellensatz, Lurking Contractions, and Contractive Determinantal Representations of Stable Polynomials

2016 ◽  
pp. 123-136 ◽  
Author(s):  
Anatolii Grinshpan ◽  
Dmitry S. Kaliuzhnyi-Verbovetskyi ◽  
Victor Vinnikov ◽  
Hugo J. Woerdeman
Keyword(s):  
Stable Polynomials

Convex combinations of G-stable polynomials

1991 ◽  
Vol 2 (3) ◽  
pp. 337-343 ◽  
Author(s):  
Marek K. Solak
Keyword(s):  
Stable Polynomials

scholarly journals Constructing convex directions for stable polynomials

2000 ◽  
Vol 45 (8) ◽  
pp. 1565-1569 ◽  
Author(s):  
A.B. Ozguler
Keyword(s):  
Stable Polynomials

On the Generation of Random Stable Polynomials

2011 ◽  
Vol 17 (2) ◽  
pp. 145-159 ◽  
Author(s):  
Pavel Shcherbakov ◽  
Fabrizio Dabbene
Keyword(s):  
Stable Polynomials

scholarly journals Local convex directions for Hurwitz stable polynomials

2002 ◽  
Vol 47 (3) ◽  
pp. 532-537
Author(s):  
A.B. Ozguler ◽  
K. Saadaoui
Keyword(s):  
Stable Polynomials ◽  
Local Convex

scholarly journals Simple necessary conditions for Hadamard factorizability of Hurwitz polynomials

2021 ◽  
Vol 37 ◽  
pp. 671-679
Author(s):  
Stanisław Białas ◽  
Michał Góra
Keyword(s):  
Necessary Conditions ◽  
Necessary Condition ◽  
Factorization Problem ◽  
Stable Polynomials ◽  
Hurwitz Polynomials

In this paper, we focus the attention on the Hadamard factorization problem for Hurwitz polynomials. We give a new necessary condition for Hadamard factorizability of Hurwitz stable polynomials of degree $n\geq 4$ and show that for $n= 4$ this condition is also sufficient. The effectiveness of the result is illustrated during construction of examples of stable polynomials that are not Hadamard factorizable.

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