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Please use this identifier to cite or link to this item: http://hdl.handle.net/1974/22

Title: Jacobian linearisation in a geometric setting
Authors: Lewis, Andrew D.
Tyner, David R.

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2003a_letter.pdf421.69 kBAdobe PDFView/Open
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:Andrew D. Lewis
Department of Mathematics and Statistics Graduate Theses

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