  We prove explit formulas for the decomposition of a differential graded Lie
algebra into a minimal and a linear $L_\infty$-algebra. We define a category of
metric $L_\infty$-algebras, called Palamodov $L_\infty$ algebras, where the
structure maps satisfy a certain convergence condition and deduce a
decomposition theorem for differential graded Lie algebras in this category.
This theorem serves for instance to prove the convergence of the Kuranishi map
assigned to a differential graded Lie algeba.
