 
Summary: Explicit WeiNorman formulæ for matrix Lie
groups via Putzer's method
Claudio Altafini
SISSAISAS
International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy;
Abstract
The WeiNorman formula locally relates the Magnus solution of a system of linear
timevarying ODEs with the solution expressed in terms of products of exponentials
by means of a set of nonlinear differential equations in the parameters of the two
types of solutions. A closed form expression of such formula is proposed based on
the use of Putzer's method.
Key words: matrix Lie groups, timevarying differential equations, Magnus
expansions, WeiNorman formula.
1 Introduction
The use of WeiNorman formulæ [28] is ubiquitous in control and systems theory, see
[6,4,13,17,9] for a few examples. Essentially, they are of importance whenever one wants
to establish local coordinates on a smooth manifold on which a finite dimensional group of
transformations is acting (the most trivial example being a matrix transition Lie group in
linear timevarying differential equations). In fact, a local chart on the manifold is induced
