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Andrew D. Lewis >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1974/22
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| Title: | Jacobian linearisation in a geometric setting |
| Authors: | Lewis, Andrew D.
Tyner, David R. |
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| Issue Date: | 2003 |
| Publisher: | IEEE |
| Citation: | Proceedings of the 42nd IEEE Conference on Decision
and Control, December 2003, pages 6084-6089 |
| Abstract: | Linearisation is a common technique in control applications, putting useful
analysis and design methodologies at the disposal of the control engineer.
In this paper, linearisation is studied from a differential geometric
perspective. First it is pointed out that the ``naïve'' Jacobian
techniques do not make geometric sense along nontrivial reference
trajectories, in that they are dependent on a choice of coordinates. A
coordinate-invariant setting for linearisation is presented to address this
matter. The setting here is somewhat more complicated than that seen in the
naïve setting. The controllability of the geometric linearisation is
characterised by giving an alternate version of the usual controllability
test for time-varying linear systems. The problems of stability,
stabilisation, and quadratic optimal control are discussed as topics for
future work |
| URI: | http://hdl.handle.net/1974/22 |
| Appears in Collections: | Mathematics & Statistics Graduate Theses
Andrew D. Lewis
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