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Functions for setting-up and solving logarithmic equations automatically

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 up previous contents
Next: Automatic controller design/synthesis functions Up: Topics for Further Improvement Previous: Generation of a -th   Contents
Miguel Attilio Torres-Torriti 2004-05-31