Title: Jacobian linearisation in a geometric setting (18 pages)
Author(s): Andrew D. Lewis and David R. Tyner
Detail: Proceedings of the 42nd IEEE Conference on Decision and Control, December 2003, pages 6084-6089
Conference proceedings version: Download

Original manuscript: 2003/03/06
Manuscript last revised: 2003/12/14

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.

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Last Updated: Thu Oct 11 08:42:18 2018

Andrew D. Lewis (andrew at mast.queensu.ca)