{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T10:11:01Z","timestamp":1698228661691},"reference-count":14,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,12,13]],"date-time":"2006-12-13T00:00:00Z","timestamp":1165968000000},"content-version":"vor","delay-in-days":4974,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory & Apps"],"published-print":{"date-parts":[[1993,5]]},"abstract":"Abstract<\/jats:title>This paper studies the problem of the stability of linear networks or systems depending polynomially on parameters when considering large values of the parameters. It has been taken into account that only the specification of nominal values and tolerances\u2014and not of actual values\u2014is physically meaningful.<\/jats:p>Algorithms to test the existence of arbitrarily large nominal values of the parameters which ensure stability either with zero tolerance, with non\u2010zero tolerances depending on the particular nominal values or with a non\u2010zero tolerance independent of the particular nominal values are proved to exist.<\/jats:p>Depending on the type of response of the above\u2010mentioned algorithms, analytic, polynomial and monomial functions\u2014in a single suitable variable\u2014that describe arbitrarily large nominal values which ensure stability in the case of zero tolerance, polynomially decreasing non\u2010zero tolerance and constant non\u2010zero tolerance respectively are proved to exist.<\/jats:p>When a monomial description with constant non\u2010zero tolerance is assured, algorithms which give the degrees and\u2014in terms of rational numbers\u2014the coefficients of the monomials and the constant non\u2010zero tolerance are proved to exist.<\/jats:p>Similar algorithms when only an analytic description with zero tolerance or a polynomial description with polynomially decreasing non\u2010zero tolerance is ensured cannot exist.<\/jats:p>","DOI":"10.1002\/cta.4490210302","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T08:46:55Z","timestamp":1183366015000},"page":"207-231","source":"Crossref","is-referenced-by-count":1,"title":["Linear networks and systems depending polynomially on parameters: Stability for large values subject to tolerance errors"],"prefix":"10.1002","volume":"21","author":[{"given":"Maurizio","family":"Ciampa","sequence":"first","affiliation":[]},{"given":"Mario","family":"Poletti","sequence":"additional","affiliation":[]},{"given":"Pierangelo","family":"Terreni","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,12,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Principles of Active Network Synthesis and Design","author":"Daryanani G.","year":"1976"},{"key":"e_1_2_1_3_2","volume-title":"Analysis and Synthesis of Linear Active Networks","author":"Mitra S. 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III"},{"key":"e_1_2_1_9_2","volume-title":"Real Algebraic and Semi\u2010algebraic Sets","author":"Benedetti R.","year":"1990"},{"key":"e_1_2_1_10_2","volume-title":"G\u00e9om\u00e9trie Alg\u00e9brique R\u00e9elle","author":"Bochnak J.","year":"1987"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(88)80016-6"},{"key":"e_1_2_1_12_2","volume-title":"Singular Points of Complex Hypersurfaces","author":"Milnor J.","year":"1968"},{"key":"e_1_2_1_13_2","unstructured":"J.Davenport Y.SiretandE.Tournier Calcul Formel. Syst\u00e8mes et Algorithms de Manipulations Alg\u00e9briques Masson Paris 1986."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-6323-4"},{"key":"e_1_2_1_15_2","volume-title":"Trait\u00e9 d'Analyse","author":"Picard \u00c9.","year":"1925"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.4490210302","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.4490210302","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T20:42:46Z","timestamp":1698180166000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.4490210302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,5]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,5]]}},"alternative-id":["10.1002\/cta.4490210302"],"URL":"https:\/\/doi.org\/10.1002\/cta.4490210302","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,5]]}}}