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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.

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This paper considers the stabilization problem for a class of nonlinear systems in the presence of mismatched disturbances. For this purpose, a differentiator is employed such that by using newly defined virtual controls and the modified error compensation signals, the command-filter backstepping approach combined with a mismatched finite-time disturbance observer such that the proposed control guarantees the asymptotic stabilization of system states. In the introduced observer, the imposed external disturbance parameters are identified precisely within the finite-time period. This produces a better transient performance compared to the Lyapunov parameter estimation method. Moreover, the imposed restrictions over external disturbances are relaxed, i.e., the common restrictive condition over the disturbances’ first derivatives is removed. This approach also helps to solve the problem of the explosion of complexity, which is usually caused by higher-order system differentiation in backstepping technique. As a result of applying this method, especially to more complicated systems, the complexity of calculation is greatly reduced. Moreover, by means of the common Lyapunov function, the stability of the proposed observer and the control scheme is shown. Finally, a simulation example is provided to show the effectiveness of the theoretical developments.