# American Institute of Mathematical Sciences

March  2016, 8(1): 99-138. doi: 10.3934/jgm.2016.8.99

## Linearisation of tautological control systems

 1 Department of Mathematics and Statistics, Queen's University, Kingston, ON K7L 3N6, Canada

Received  May 2014 Revised  October 2015 Published  February 2016

The framework of tautological control systems is one where control'' in the usual sense has been eliminated, with the intention of overcoming the issue of feedback-invariance. Here, the linearisation of tautological control systems is described. This linearisation retains the feedback-invariant character of the tautological control systems framework and so permits, for example, a well-defined notion of linearisation of a system about an equilibrium point, something which has surprisingly been missing up to now. The linearisations described are of systems, first, and then about reference trajectories and reference flows.
Citation: Andrew D. Lewis. Linearisation of tautological control systems. Journal of Geometric Mechanics, 2016, 8 (1) : 99-138. doi: 10.3934/jgm.2016.8.99
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