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Matematicheskie Zametki, 2014, Volume 96, Issue 4, Pages 596–608
DOI: https://doi.org/10.4213/mzm9367 (Mi mzm9367) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Qualitative Properties of Differential-Algebraic Equations

V. F. Chistyakova, Ta Duy Phuongb

a Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk
b Hanoi Institute of Mathematics
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DOI: https://doi.org/10.4213/mzm9367
Abstract: Linear systems of ordinary differential equations with identically degenerate coefficient matrix before the derivative of the unknown vector function are considered. The structure of general solutions and the notion of singular point of such systems are discussed. From the comparison of the properties of the “perturbed” and original problems, a sufficient criterion for the Lyapunov asymptotic stability of the zero solution is obtained.
Keywords: differential-algebraic equation, Lyapunov stability, Lyapunov asymptotic stability, regularizing operator, Euler difference scheme, Kronecker–Capelli condition.
Received: 24.01.2012
English version:
Mathematical Notes, 2014, Volume 96, Issue 4, Pages 563–574
DOI: https://doi.org/10.1134/S0001434614090314
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: V. F. Chistyakov, Ta Duy Phuong, “On Qualitative Properties of Differential-Algebraic Equations”, Mat. Zametki, 96:4 (2014), 596–608; Math. Notes, 96:4 (2014), 563–574
Citation in format AMSBIB
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