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1993•IEEE Transactions on Automatic ControlRequires access

Root distribution of a polynomial in subregions of complex plane

J.S.H. Tsai, S.S. Chen

Open publisher page 9 citations

Abstract

Modified processes are proposed for directly treating singularities in the Routh array, and procedures are developed for determining the respective orders of simple and/or repeated roots lying on the imaginary axis. The extended Sturm test is developed for determining the root distribution on some specified lines. Moreover, to enhance the Routh stability theorem, the extended Routh theorem for finding the numbers of roots of a polynomial lying within some specified regions is proposed.>

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What this paper is about

Modified processes are proposed for directly treating singularities in the Routh array, and procedures are developed for determining the respective orders of simple and/or repeated roots lying on the imaginary axis. The extended Sturm test is developed for determining the root distribution on some specified lines. Moreover, to enhance the Routh stability theorem, the extended Routh theorem for finding the numbers of roots of a polynomial lying within some specified regions is proposed.>

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OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Modified processes are proposed for directly treating singularities in the Routh array, and procedures are developed for determining the respective orders of simple and/or repeated roots lying on the imaginary axis. The extended Sturm test is developed for determining the root distribution on some specified lines. Moreover, to enhance the Routh stability theorem, the extended Routh theorem for finding the numbers of roots of a polynomial lying within some specified regions is proposed.>

Key concepts: Complex plane, Routh–Hurwitz stability criterion, Properties of polynomial roots, Polynomial, Mathematics, Gravitational singularity, Root (linguistics), Distribution (mathematics)

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