On differential structures of polynomial spaces in control theory

Baltazar Aguirre Hernández, Martn Eduardo Frías-Armenta, Fernando Verduzco

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


A valuable number of works has been published about Hurwitz and Schur polynomials in order to known better their properties. For example it is known that the sets of Hurwitz and Schur polynomials are open and no convex sets. Besides, the set of monic Schur polynomials is contractible. Now we study this set using ideas from differential topology, and we prove that the space of Schur complex polynomials with positive leading coefficient, and the space of Hurwitz complex polynomials which leading coefficient having positive real part, have structure of trivial vector bundle, and each space of (Schur complex and real, Hurwitz complex) polynomials has a differential structure diffeomorphic to some known spaces.

Original languageEnglish
Pages (from-to)372-382
Number of pages11
JournalJournal of Systems Science and Systems Engineering
Issue number3
StatePublished - Sep 2012

Bibliographical note

Funding Information:
This work is partly supported by CONACYT CB-2010/150532.


  • Hurwitz complex polynomials
  • Schur polynomials
  • trivial vector bundle


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