{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,25]],"date-time":"2024-05-25T14:10:07Z","timestamp":1716646207126},"reference-count":31,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J CIRCUIT SYST COMP"],"published-print":{"date-parts":[[2014,7]]},"abstract":"<jats:p>In this paper, we extend the topological formulae of Maxwell and Kirchhoff, characterizing the non-singularity of node-admittance and loop-impedance matrices, to mixed problems, that is, to circuits combining admittance and impedance descriptions or, in nonlinear cases, involving both voltage- and current-controlled resistors. By means of this mixed formula we analyze the index of differential-algebraic models of nonlinear uncoupled circuits in a very broad setting, namely, without assumptions on their topology, their passivity or the controlling variables for nonlinear resistors. In particular, our approach allows for a characterization of index two circuits in topologically degenerate settings, which had been so far elusive in the non-passive context. As a byproduct we address the unique solvability of mixed resistive circuits, a problem which also arises in connection to the so-called DC-solvability condition of dynamic circuits. For the sake of brevity, we discuss in less detail how to extend the analysis to problems with mixed descriptions in reactive devices.<\/jats:p>","DOI":"10.1142\/s021812661450087x","type":"journal-article","created":{"date-parts":[[2014,3,31]],"date-time":"2014-03-31T06:05:53Z","timestamp":1396245953000},"page":"1450087","source":"Crossref","is-referenced-by-count":1,"title":["INDEX AND SOLVABILITY OF UNCOUPLED CIRCUITS: A CHARACTERIZATION WITHOUT RESTRICTIONS ON THEIR PASSIVITY, TOPOLOGY OR CONTROLLING STRUCTURE"],"prefix":"10.1142","volume":"23","author":[{"given":"IGNACIO GARC\u00cdA","family":"DE LA VEGA","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a las Tecnolog\u00edas de la Informaci\u00f3n, Escuela T\u00e9cnica Superior de Ingenieros de Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RICARDO","family":"RIAZA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada a las Tecnolog\u00edas de la Informaci\u00f3n, Escuela T\u00e9cnica Superior de Ingenieros de Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,5,14]]},"reference":[{"key":"rf1","volume-title":"Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations","author":"Brenan K. 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