Delayed-feedback control of oscillations in non-linear planar systems

The use of delayed feedback of position for the control of oscillatory behaviour is analysed. It is shown that linear feedback can annihilate limit cycles and stabilize the origin. Furthermore, it is possible to create an asymptotically stable limit cycle with any prescribed amplitude using a simple non-linear feedback. For almost all values of the delay, these feats can be achieved without using derivative information in the feedback. The results indicate a possible mechanism by which biological systems accomplish complex control tasks using delayed and partial state information.