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Despite that the synchronization of chaotic systems has been extensively investigated and demonstrated to contribute to physical, chemical, financial, and biological applications, the synchronization of different perturbed bistable systems appears to be an open issue. This is significant with the fact that the bistability widely exists from the visual perception to the electrical and mechanical systems. Therefore, this paper proposes a continuous finite-time terminal sliding mode control method to synchronize two bistable electromechanical transducers, with the electrostatic one acting as the master system and the piezoelectric one acting as the slave system. The model of two systems as well as the control method considering external disturbances and unmodeled dynamics are presented. Numerical simulation results show that two bistable systems can be synchronized with our proposed control method in intrawell, chaotic, and interwell oscillation modes. Furthermore, the chattering issue in conventional discontinuous controllers is eliminated with our designed continuous finite-time terminal protocols for bistable chaotic systems so as to improve the robustness of the controller and avoid its failure. Interesting findings are discussed for the varying system responses and control inputs in different oscillation modes. This work also is expected to facilitate the development of applications where bistability is found such as power or communication systems to resist the external disturbances. [ABSTRACT FROM AUTHOR]

In this paper, fast global fixed-time terminal sliding mode control for the synchronization problem of a generalized class of nonlinear perturbed chaotic systems has been investigated with the application of memristor-based oscillator in the presence of external disturbances and unmodeled dynamics. In the fixed-time control strategy, unlike conventional asymptotic or finite-time approaches, convergence time is not related to the initial conditions. In the designed global fixed-time controller, both the sliding phase and reaching phase have fixed-time convergence characteristics and consequently, via the proposed strategy, precise synchronization of the master-slave systems is accomplished within fixed convergence time. The fast fixed-time synchronization problem of the nonlinear memristor chaotic system (MCS) has been investigated. In the first stage, an in-circuit emulator (ICE) for the considered memristor is utilized in order to apply on the defined MCSs. In the next stage, according to the considered ICE, the dynamical structure of the MCS is formulated along with the fixed-time synchronization problem which is efficiently addressed via the designed controller in the presence of external disturbances and unmodeled dynamics. Finally, the strength and validity of the theoretical outcomes are confirmed through numerical simulations. [ABSTRACT FROM AUTHOR]