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Mat. Zametki, 2014, Volume 96, Issue 4, Pages 596–608 (Mi mz9367)  

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

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.

DOI: https://doi.org/10.4213/mzm9367

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English version:
Mathematical Notes, 2014, 96:4, 563–574

Bibliographic databases:

Document Type: Article
UDC: 517.518
Received: 24.01.2012

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

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