| Summary: | Limitations of the delayed feedback control and of its extended versions have been fully treated in the literature. The oscillating delayed feedback control appears as a promising scheme to overcome this problem. Two methods based on it are dealt with in this work. It is rigorously proven that for a nonlinear scalar system, stabilization in one of its (unstable) equilibrium points is achieved if any of these methods is applied. An ad-hoc map is associated to the (continuous) controlled system and the results are derived using discrete-time system stabilization tools. Moreover, the stability parameters region is fully described and issues like control performance, rate of convergence or robustness aspects are carefully analyzed.
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