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On Criteria for Asymptotic Stability of Differential‐Algebraic Equations
Author(s) -
Stykel T.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200203)82:3<147::aid-zamm147>3.0.co;2-h
Subject(s) - mathematics , eigenvalues and eigenvectors , matrix pencil , exponential stability , numerical stability , differential algebraic equation , algebraic number , differential algebraic geometry , differential equation , stability (learning theory) , pencil (optics) , mathematical analysis , matrix differential equation , algebraic equation , stability theory , numerical analysis , ordinary differential equation , nonlinear system , computer science , physics , quantum mechanics , machine learning
This paper discusses Lyapunov stability of the trivial solution of linear differential‐algebraic equations. As a criterion for the asymptotic stability we propose numerical parameters characterizing the property of a regular matrix pencil λ A – B to have all finite eigenvalues in the open left half‐plane. Numerical aspects for computing these parameters are discussed.