A stability result for delayed feedback controllers

We consider the delayed feedback control (DFC) scheme for one dimensional discrete time systems. To analyze the stability, we construct a map whose fixed points correspond to the periodic orbits of the system to be controlled. Then the stability of the DFC is equivalent to the stability of the corresponding equilibrium point of the constructed map. We obtain a formula for the characteristic polynomial of the Jacobian of this map. Then the Schur stability of this polynomial could be used to analyze the stability of DFC. We also present some simulation results.