Continuous robust controller with fixed convergence time for synchronization of perturbed nonlinear transducers

The synchronization of two chaotic electrostatic and electromechanical transducers is addressed via a continuous terminal sliding-mode control (SMC) strategy. Recently, fixed-time convergence has received increased attention among scholars. The convergence time with this type of controller has an upper bound independent of the initial conditions. In this regard, two fixed-time sliding variables are proposed to design a robust continuous controller having a fixed-time convergence feature. Then, a robust SMC control is formulated to steer the error states onto the sliding surfaces despite the external disturbances and model uncertainties. Due to the continuous structure of the designed strategy, the proposed controller is chattering-free, which is essential in many practical applications. The convergence proof for the continuous robust controller based on the Lyapunov stability theory has been presented. Finally, a comparison of the proposed approach with existing methods has been illustrated through simulation results to demonstrate its superiority.