Geodesic
Regular systems of differential-algebraic equations
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 4, pp. 107-127

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We consider linear and nonlinear systems of differential-algebraic equations. The conditions of reducibility and regularity of linear systems are obtained. The theorems connecting these notions are proved. The theorem about stability of nonlinear systems in the first approximation is proved under the conditions of existence of some global structural form. An arbitrary high unsolvability index and variable ranks of Jacobi matrices describing a system are allowed.
Keywords: differential-algebraic equations, reducibility, regularity, stability in the first approximation. 
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     title = {Regular systems of differential-algebraic equations},
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A. A. Shcheglova; P. S. Petrenko. Regular systems of differential-algebraic equations. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 4, pp. 107-127. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_4_a7/