Root Distribution of a Polynomial in Subregions of the Complex Plane

Jason S.H. Tsai, Shyan S. Chen

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Newly modified processes are proposed for directly treating singularities in the Routh array, and new 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, we propose the extended Routh theorem for finding the numbers of roots of a polynomial lying within some specified regions.

Original languageEnglish
Pages (from-to)173-178
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - 1993 Jan

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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