Controlling high-dimensional unstable steady states using delay, duration and feedback

We present a control method for stabilizing steady states using only discrete pulses of an available system parameter. In addition to the feedback amplitude of the pulse, we employ the pulse width and delay as additional parameters. This allows us to stabilize steady states with more than one unstable direction and prevent unwanted transients in the high-dimensional stable subspace. We have applied our method to a model of a multimode laser whose steady state becomes unstable due to a Hopf bifurcation and may exhibit periodic oscillations and chaos, We also show the importance of considering the delay between the system measurement and application of control that will be present in any real experiment.