Presetting-time complete synchronization of two Lorenz systems with applications into nonlinear PMSMs and Hindmarsh-Rose neuron models

Abstract This paper begins by examining the presetting-time synchronization (PtS) of two nonlinear Lorenz systems and subsequently applies these findings to synchronize the permanent magnet synchronous motors (PMSMs) and Hindmarsh-Rose neuron models. Unlike conventional finite-time synchronization (FtS) or fixed-time synchronization (FxS) methods, the upper bound estimation of convergence time (UBECT) in this study can be predefined as a constant, unaffected by initial conditions or control parameters. Furthermore, the control schemes developed here are free from chattering, as they avoid using traditional discontinuous signum and absolute value functions. Through classical Lyapunov stability analysis, sufficient conditions are derived to ensure PtS between nonlinear Lorenz systems, PMSMs, and Hindmarsh-Rose neuron models. Lastly, numerical simulations are conducted to confirm the accuracy and efficiency of the theoretical findings, with comparisons and perturbation analyses also included.