The main direction of the laboratory's research is the analysis and synthesis of phase-locked loop systems and their application in information control systems (telecommunications equipment, distributed computer architectures, global navigation satellite systems, gyroscopes and other applications). PLL circuits are nonlinear automatic control systems that implement the master-slave principle of synchronizing the phases of periodic signals.

Main publications.

1. N.V. Kuznetsov, M.Y. Lobachev, Exact pull-In range and the hidden boundary of global stability for PLL with lead-lag filter, IEEE Access, 13, 2025, 94785-94821 (https://doi.org/10.1109/ACCESS.2025.3573693)
2. N.V. Kuznetsov, M.Y. Lobachev, E.V. Kudryashova, O.A. Kuznetsova, D.G. Arseniev, The Viterbi problem on coincidence of phase-locked loop lock-in, pull-in, and hold-in ranges, Nonlinear Dynamics, 113, 2025, 13771-13789, 2025 (https://doi.org/10.1007/s11071-025-11040-3)
3. N.V. Kuznetsov, M.Y. Lobachev, M.V. Yuldashev, R.V. Yuldashev, M.S. Tavazoei, The Gardner Problem on the Lock-In Range of Second-Order Type 2 Phase-Locked Loops, IEEE Transactions on Automatic Control, 2023 (https://doi.org/10.1109/TAC.2023.3277896)
4. N.V. Kuznetsov, M.Y. Lobachev, T.N. Mokaev, Hidden boundary of global stability in a counterexample to the Kapranov conjecture on the pull-in range, Doklady Mathematics, 108, 2023, 300-308 (https://doi.org/10.1134/S1064562423700898)
5. N.V. Kuznetsov, Y.V. Belyaev, A.V. Styazhkina, M.V. Yuldashev, R.V. Yuldashev, Effects of PLL Architecture on MEMS Gyroscope Performance, Gyroscopy and Navigation, 13(1), 2022, 44-52 (https://doi.org/10.1134/S2075108722010047)
6. N.V. Kuznetsov, A.S. Matveev, M.V. Yuldashev, R.V. Yuldashev, Nonlinear Analysis of Charge-Pump Phase-Locked Loop: The Hold-In and Pull-In Ranges, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 68, no. 10, 2021, pp. 4049-4061 (https://doi.org/10.1109/TCSI.2021.3101529)
7. N.V. Kuznetsov, M.Y. 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 Mathematics, 103(3):157–161, 2021
8. N.V. Kuznetsov, M.Y. Lobachev, M.V. Yuldashev, R.V. Yuldashev, The Egan problem on the pull-in range of type 2 PLLs, IEEE Transactions on Circuits and Systems II: Express Briefs, 2020, (http://dx.doi.org/10.1109/TCSII.2020.3038075)
9. N.V. Kuznetsov, G.A. Leonov, M.V. Yuldashev, R.V. Yuldashev, Hidden attractors in dynamical models of phase-locked loop circuits: limitations of simulation in MATLAB and SPICE, Communications in Nonlinear Science and Numerical Simulation, vol. 51, 2017, pp. 39-49 (http://dx.doi.org/10.1016/j.cnsns.2017.03.010)
10. R.E. Best, N.V. Kuznetsov, G.A. Leonov, M.V. Yuldashev, R.V. Yuldashev, Tutorial on dynamic analysis of the Costas loop, IFAC Annual Reviews in Control, 42, 2016, pp. 27-49 (http://dx.doi.org/10.1016/j.arcontrol.2016.08.003)
11. G.A. Leonov, N.V. Kuznetsov, M.V. Yuldashev, R.V. Yuldashev, Hold-in, pull-in, and lock-in ranges of PLL circuits: rigorous mathematical definitions and limitations of classical theory, IEEE Transactions on Circuits and Systems I: Regular Papers, 62(10), 2015, art. num. 7277189, pp.2454-2464 (http://dx.doi.org/10.1109/TCSI.2015.2476295)
12. G.A. Leonov, N.V. Kuznetsov, Nonlinear Mathematical Models of Phase-Locked Loops. Stability and Oscillations, Vol. 7, Cambridge Scientific Publisher, 2014 (ISBN 978-1-908106-38-4)