Supplementary material for Generic stabilisability for time-delayed feedback control

Author: Jan Sieber

This folder contains Matlab code and its output for illustrating examples used in

Jan Sieber (2016): Generic stabilizability for time-delayed feedback control, Proc. R. Soc. A 20150593. (doi:10.1098/rspa.2015.0593),

Preprint download: arxiv:1508.05671.
Download a zip of all supplementary files, including Matlab/octave source code, from figshare: doi:10.6084/m9.figshare.2993812.

List of Matlab scripts and their outputs:

Hopf example output (html): published Matlab output of HopfExample.m script. This shows the Matlab code with formatted comments and graphs similar to the example section in the paper.
Output (html) for demo ParametricPendulum.m using extended time-delayed feedback (ETDF) control to stabilise unstable oscillations in a parametrically excited pendulum.

List of Matlab functions used in the demonstration scripts:

SpecExpAssign.m: computes gains K to assign spectrum of matrix P exp(bK) for nxn matrix P and nx1 vector b.
etdf_controlled_rhs.m: wrapper around right-hand side f (in x=f(x,p,u)) to make it fit into DDE-Biftool's format
etdf_control.m: constructs ETDF gains for asymptotic parameters and compute true stability
gain_of_x.m: convert gain as contructed by Brunovsky to true x-dependent gain K(x)

Note that the Matlab functions and scripts rely on DDE-Biftool 3.1, available here: sourceforge.net/projects/ddebiftool.