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Continuity argument revisited : geometry of root clustering via symmetric products

Continuity argument revisited : geometry of root clustering via symmetric products

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

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

<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/44918"> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-02-07T14:27:55Z</dcterms:available> <dcterms:issued>2016</dcterms:issued> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/44918"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-02-07T14:27:55Z</dc:date> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <dcterms:rights rdf:resource="https://kops.uni-konstanz.de/page/termsofuse"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/52"/> <dc:contributor>Violet, Grey</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:creator>Violet, Grey</dc:creator> <dc:language>eng</dc:language> <dc:rights>terms-of-use</dc:rights> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/44918/3/Violet_2-1mkk6smbq4w784.pdf"/> <dcterms:title>Continuity argument revisited : geometry of root clustering via symmetric products</dcterms:title> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/44918/3/Violet_2-1mkk6smbq4w784.pdf"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/52"/> </rdf:Description> </rdf:RDF>

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