Linearisation of tautological control systems

Andrew D. Lewis

doi:10.3934/jgm.2016.8.99

Article Contents

2016, Volume 8, Issue 1: 99-138. Doi: 10.3934/jgm.2016.8.99

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Linearisation of tautological control systems

Andrew D. Lewis^1,

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

Received: April 30, 2014

Revised: September 30, 2015

Published: February 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 93A30, 93B18; Secondary: 46E10, 93B99.

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