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In the case when the Lie algebra is non-nilpotent an approximation,
such as truncation of the series expansion of the exponential operator
will be necessary in any attempt to determine an explicit expression
for the Wei-Norman equations. The automatic identification of the
convergence of a series to a given function is in general a very
difficult problem and one of the main obstacles to the implementation
of an exact explicit solution.
If the system is non-nilpotent but has a finite-dimensional Lie
algebra and allows a representation as a system on a matrix Lie
group, then there exists the possibility to obtain explicit
expressions of the Wei-Norman equations using the approach proposed
in [2].
It would also be convenient to develop concurrently some routines for
the nilpotentization of the system by state feedback and
state-space transformations, since working with the nilpotent version of
the system would allow to obtain an explicit Wei-Norman formula.
Next: Automatic controller design/synthesis functions
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Miguel Attilio Torres-Torriti
2004-05-31