We address the problem which type of initial state yields successful stabilisation when time-delayed feedback control is applied. Using well known concepts from bifurcation theory we provide a general mechanism that limits the corresponding basins of attraction. Application of normal form analysis to general delay-differential equations proves the universality of our results. The empirical criteria which determine the prospective size of the basin are easily accessible and a demonstration in terms of a simple numerical simulation is provided. © 2004 Elsevier B.V. All rights reserved.
Just, W., Benner, H., & Von Loewenich, C. (2004). On global properties of time-delayed feedback control: Weakly nonlinear analysis. In Physica D: Nonlinear Phenomena (Vol. 199, pp. 33–44). https://doi.org/10.1016/j.physd.2004.08.002