  We give sufficient conditions, on data including the monodromy
representation, the Stokes matrices and the Poincare ranks at prescribed
singularities, to solve the generalized Riemann-Hilbert problem with irregular
singularities. We recover in particular the irreducibility condition on the
monodromy given by Bolibrukh and Kostov in the classical case. We apply the
above criteria to solve the inverse problem in differential Galois theory with
a better control of the singularities.
