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Explicit Wei-Norman formul for matrix Lie groups via Putzer's method

Summary: Explicit Wei-Norman formulŠ for matrix Lie
groups via Putzer's method
Claudio Altafini
International School for Advanced Studies
via Beirut 2-4, 34014 Trieste, Italy;
The Wei-Norman formula locally relates the Magnus solution of a system of linear
time-varying 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, time-varying differential equations, Magnus
expansions, Wei-Norman formula.
1 Introduction
The use of Wei-Norman formulŠ [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 time-varying differential equations). In fact, a local chart on the manifold is induced


Source: Altafini, Claudio - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)


Collections: Engineering; Mathematics