Predefined-time stabilization of Lorenz system with applications for stabilizing and synchronizing chaotic finance systems

Abstract

This article investigates the predefined-time stabilization (PtS) of the canonical Lorenz system at first, and then applies the derived results into the chaotic finance systems (CFSs) so as to realize the stabilization and synchronization, respectively. Compared with the traditional finite-/fixed-time stability analysis, the upper-bound of convergence time (UbCT) in this investigation can be set beforehand in need, which is an explicit constant regardless of initial values, system dimension, and controlling parameters. Moreover, the designed control schemes are non-chattering, which do not contain the conventional discontinuous signum and absolute value functions anymore. Via adopting the second Lyapunov method, the sufficient conditions are obtained successively for guaranteeing the realization of PtS for Lorenz system, CFS, as well as the predefined-time synchronization between two CFSs. The numerical experiments are finally arranged to manifest the correctness and effectiveness of the theoretical fruits, in which some comparison and perturbation analysis are made.