scholarly journals Retracted: On the Interlacing Property and the Routh-Hurwitz Criterion

2020 ◽  
Vol 2020 ◽  
pp. 1-1
Author(s):  
International Journal of Mathematics and Mathematical Sciences
Keyword(s):  
Interlacing Property

scholarly journals An eigenvector interlacing property of graphs that arise from trees by Schur complementation of the Laplacian

2013 ◽  
Vol 438 (3) ◽  
pp. 1078-1094 ◽  
Author(s):  
Alexander R. Griffing ◽  
Benjamin R. Lynch ◽  
Eric A. Stone
Keyword(s):  
Interlacing Property

A new distortion measure for spectral quantization based on the LSF intermodel interlacing property

2001 ◽  
Vol 35 (3-4) ◽  
pp. 191-202 ◽  
Author(s):  
Mi Suk Lee ◽  
Hong Kook Kim ◽  
Hwang Soo Lee
Keyword(s):  
Distortion Measure ◽  
Interlacing Property

Interlacing Properties for Mass-Dashpot-Spring Systems With Proportional Damping

2004 ◽  
Vol 126 (2) ◽  
pp. 426-430 ◽  
Author(s):  
Jong-Lick Lin ◽  
Kuo-Chin Chan ◽  
Jyh-Jong Sheen ◽  
Shin-Ju Chen
Keyword(s):  
Real Axis ◽  
Nonlinear Mapping ◽  
Root Locus ◽  
Input Matrix ◽  
Column Space ◽  
Transmission Zeros ◽  
Output Matrix ◽  
Spring System ◽  
Interlacing Property ◽  
Zeros And Poles

A mass-dashpot-spring system with proportional damping is considered in this paper. On the basis of an appropriate nonlinear mapping and the root-locus technique, the interlacing property of transmission zeros and poles is investigated if the columns of the input matrix are in the column space generated by the transpose of the output matrix. It is verified that transmission zeros interlace with poles on a specific circle and the nonpositive real axis segments for a proportional damping system. Finally, three examples are given to illustrate the property.

Checking the parity interlacing property via the Sturm algorithm

1991 ◽  
Vol 22 (1) ◽  
pp. 189-196
Author(s):  
JUHNG-PERNG SU ◽  
JER-GUANG HSIEH ◽  
MING-HUEI LIN
Keyword(s):  
Interlacing Property

scholarly journals On the interlacing property and the Routh-Hurwitz criterion

2003 ◽  
Vol 2003 (12) ◽  
pp. 727-737 ◽  
Author(s):  
Ziad Zahreddine
Keyword(s):  
Simple Proof ◽  
Stability Theory ◽  
Mathematical Community ◽  
Interesting Property ◽  
Important Criterion ◽  
Stability Criteria ◽  
Root Locus ◽  
Nyquist Criterion ◽  
Interlacing Property

Unlike the Nyquist criterion, root locus, and many other stability criteria, the well-known Routh-Hurwitz criterion is usually introduced as a mechanical algorithm and no attempt is made whatsoever to explain why or how such an algorithm works. It is widely believed that simple derivations of this important criterion are highly requested by the mathematical community. In this paper, we address this problem and provide a simple proof of the Routh-Hurwitz criterion based on two generalizations of an interesting property known in stability theory as the interlacing property. Within the same context, the singularities that may arise in the Routh-Hurwitz criterion are also dealt with.

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