Continuity argument revisited : geometry of root clustering via symmetric products

Violet, Grey

Continuity argument revisited : geometry of root clustering via symmetric products

Dateien

Violet_2-1mkk6smbq4w784.pdfGröße: 851.07 KBDownloads: 202

Datum

2016

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Zukunftskolleg
Mathematik und Statistik

Publikationstyp

Preprint

Publikationsstatus

Published

Zusammenfassung

We study the spaces of polynomials stratified into the sets of polynomial with fixed number of roots inside certain semialgebraic region Ω, on its border, and at the complement to its closure. Presented approach is a generalisation, unification and development of several classical approaches to stability problems in control theory: root clustering (D-stability) developed by R.E. Kalman, B.R. Barmish, S. Gutman et al., D-decomposition(Yu.I. Neimark, B.T. Polyak, E.N. Gryazina) and universal parameter space method(A. Fam, J. Meditch, J.Ackermann). Our approach is based on the interpretation of correspondence between roots and coefficients of a polynomial as a symmetric product morphism. We describe the topology of strata up to homotopy equivalence and, for many important cases, up to homeomorphism. Adjacencies between strata are also described. Moreover, we provide an explanation for the special position of classical stability problems: Hurwitz stability, Schur stability, hyperbolicity.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Optimization and Control; Algebraic Geometry; Geometric Topology; Rings and Algebras

Zitieren

ISO 690

VIOLET, Grey, 2016. Continuity argument revisited : geometry of root clustering via symmetric products

BibTex

@unpublished{Violet2016Conti-44918,
  year={2016},
  title={Continuity argument revisited : geometry of root clustering via symmetric products},
  author={Violet, Grey}
}

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