# Controlling Discrete Systems via Time-Delay Feedback

## Ilan Harrington

We study a matrix form of time-delay feedback control in the context of discrete time maps of high dimension. In almost all cases where standard
proportional feedback control methods can achieve control, time-delay feedback
controllers containing only passive elements can be designed to achieve
identical linear stability properties.
Analysis of an example involving a ring of coupled maps that can be
controlled at only two sites demonstrates that the time-delay controller
equivalent to a standard optimal controller can be equally robust in the
presence of noise, except at special points in parameter space where the
uncontrolled system has a mode with Floquet multiplier exactly equal to 1.
Numerical simulations confirm the results of the analysis.

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