Geodesic
On the generalized Gardner problem for phase-locked loops in electrical grids
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 71-75

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Methods of nonlinear analysis and synthesis of synchronization control systems for electrical grids have been developed. The use of averaging methods and Lyapunov-type stability criteria for the cylindrical phase space have made it possible for the first time in the Gardner problem to obtain analytical estimates of the system parameters to ensure acceptable values of phase errors and to take into account changes in the reference signal amplitude.
Keywords: phase-locked loop, tunable lock-in range, Lyapunov function, Gardner problem, electrical grids. 
@article{DANMA_2021_498_a13,
     author = {N. Kuznetsov and M. Yu. Lobachev and M. V. Yuldashev and R. V. Yuldashev and S. I. Volskiy and D. A. Sorokin},
     title = {On the generalized {Gardner} problem for phase-locked loops in electrical grids},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {71--75},
     publisher = {mathdoc},
     volume = {498},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_498_a13/}
}
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N. Kuznetsov; M. Yu. Lobachev; M. V. Yuldashev; R. V. Yuldashev; S. I. Volskiy; D. A. Sorokin. On the generalized Gardner problem for phase-locked loops in electrical grids. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 71-75. http://geodesic.mathdoc.fr/item/DANMA_2021_498_a13/