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Global unique solvability for memristive circuit DAEs of Index 1
Author(s) -
Jansen Lennart,
Matthes Michael,
Tischendorf Caren
Publication year - 2015
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.1927
Subject(s) - monotonic function , mathematics , nonlinear system , passivity , control theory (sociology) , implicit function theorem , function (biology) , modified nodal analysis , differential algebraic equation , algebraic number , topology (electrical circuits) , index (typography) , computer science , differential equation , mathematical analysis , ordinary differential equation , nodal , engineering , combinatorics , control (management) , artificial intelligence , world wide web , medicine , physics , anatomy , quantum mechanics , evolutionary biology , electrical engineering , biology
Known solvability results for nonlinear index‐1 differential‐algebraic equations (DAEs) are in general local and rely on the Implicit Function Theorem. In this paper, we derive a global result which guarantees unique solvability on a given time interval for a certain class of index‐1 DAEs with certain monotonicity conditions. Based on this result, we show that memristive circuit DAEs arising from the modified nodal analysis are uniquely solvable if they fulfill certain passivity and network topological conditions. Furthermore we present an error estimation for the solution with respect to perturbations on the right‐hand side and in the initial value. Copyright © 2013 John Wiley & Sons, Ltd.