{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:03:11Z","timestamp":1787320991847,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>The present paper addresses stability properties of singular equilibria arising in a given family of quasi-linear ODEs. These ODEs model continuous-time methods for root-finding problems and their singular equilibria are degenerate in the sense that the linearization of the system at equilibrium yields a singular matrix pencil. The analysis is based upon a normal form defined by a codimension-one regular system coupled with a singular scalar equation. The key step is the formulation of certain codimension-one Lyapunov matrix equations which incorporate the relevant singular information and allow for the construction of Lyapunov functions supporting the stability analysis. This approach makes it possible to state precisely the asymptotic stability of such degenerate equilibria, and provides a local estimation of the corresponding attraction domains. An application to the computation of singular DC operating points in nonlinear circuits is discussed.<\/jats:p>","DOI":"10.1137\/s0036141003425003","type":"journal-article","created":{"date-parts":[[2008,2,5]],"date-time":"2008-02-05T11:34:21Z","timestamp":1202211261000},"page":"678-690","source":"Crossref","is-referenced-by-count":4,"title":["Attraction Domains of Degenerate Singular Equilibria in Quasi-linear ODEs"],"prefix":"10.1137","volume":"36","author":[{"given":"Ricardo","family":"Riaza","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61257-2"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1515\/9783110853698"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479800378660"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/17\/1\/015"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(97)00084-8"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490170207"},{"key":"R7","unstructured":"L. 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Boche,\n                      A normal form for implicit differential equations near singular points\n                      , in Proceedings of ECCTD\u201997, Budapest, Hungary, Vol. 2, 1997, pp. 1048\u20131053."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2002.805739"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019711532679"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"R. Riaza,\n                      Preliminary normal forms for a class of singular equilibria in implicit ODEs\n                      , in Nonlinear Analysis and Applications, R. Agarwal and D. 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Venkatasubramanian,\n                      A Taxonomy of the Dynamics of Large Differential Algebraic Systems such as the Power System\n                      , Ph.D. thesis, Washington University, St. Louis, 1992."}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036141003425003","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:02:57Z","timestamp":1787317377000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036141003425003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1137\/S0036141003425003"],"URL":"https:\/\/doi.org\/10.1137\/s0036141003425003","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}