Geodesic
On the fundamental matrix of a~Pfaffian system of Fuchsian type
Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1031-1054

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A necessary and sufficient condition is given in order that a completely integrable Pfaffian system with regular singular point, given on a polydisk $D^n$, be of Fuchsian type. It is proved that the system is Fuchsian if and only if the space of solutions is “weakly singular”. In the one-dimensional case, this problem was studied by A. H. M. Levelt (RZhMat., 1963, 12B56). For higher dimensions, a similar attempt was made by R. Gérard (RZhMat., 1970, IA553), but his paper contains an error. Bibliography: 4 titles. 
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     author = {A. A. Bolibrukh},
     title = {On the fundamental matrix of {a~Pfaffian} system of {Fuchsian} type},
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A. A. Bolibrukh. On the fundamental matrix of a~Pfaffian system of Fuchsian type. Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1031-1054. http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a6/