Abstract
In this paper, a transformation which connects the matrices of the Hermite and Sehur—Cohn criteria– for root distribution is obtained. Based on this transformation, the relationship between the reduced Hermite and reduced Schur–Cohn criteria is also obtained. Furthermore, the transformation which connects the Lienard—Chipart stability criterion and the simplified determinantal stability criterion for the unit circle is derived. Finally, the connection between the inner form of the Hermite and Schur7ndash;Cohn criteria is established. The importance of the various transformations lies in the fact that their existence implies that a proof of one left7ndash;half–plane stability criterion immediately yields a proof of a corresponding unit circle criterion, and conversely. The various matrix transformations are obtained from the matrix transformation linking vectors of the coefficients of two polynomials whose respective root distributions are studied and which are related by a bilinear transformation of the underlying variables. The symmetry and skew symmetry of the matrix transformation are utilized to obtain the various transformations derived in this paper
Published Version
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