Delayed feedback stabilization of unstable equilibria

Леонов, Г. А.; Shumafov, M. M.; Kuznetsov, Nikolay

doi:10.3182/20140824-6-za-1003.02458

Cited by 7 publications

(2 citation statements)

References 27 publications

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“…These strategies may be developed to stabilize equilibrium points in the n-dimensional case under adequated observability and controlability conditions without presenting the restrictions of the DFC methods studied in [15] and [30]. More interestingly a suitable extension of our second method appears as a candidate for overcoming the ONL, coming out an alternative of [19] and [23].…”

Section: Concluding Remarks and Future Researchmentioning

confidence: 99%

“…This index of convergence and a detailed analysis of the stability parameters region confirm the claimed conjectures. These strategies may be developed to stabilize equilibrium points in the n-dimensional case under adequated observability and controlability conditions without presenting the restrictions of the DFC methods studied in [7] and [12]. More interestingly a right extension of our second method appears as a candidate for overcoming the ONL, coming out as an alternative of [8] in which there is also an "on-off switching" feedback gain but it does not work in the one dimensional case.…”

Section: Concluding Remarks and Future Researchmentioning

confidence: 99%

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Oscillating delayed feedback control schemes for stabilizing equilibrium points

Pastor

González

2019

Heliyon

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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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