Synchronization problem for a class of multi-input multi-output systems with terminal sliding mode control based on finite-time disturbance observer: Application to Chameleon chaotic system

Abstract This paper studies the synchronization problem of two nonlinear multi-input multi-output (MIMO) systems in finite-time period. For this purpose, a terminal sliding mode controller (TSMC) with a finite-time disturbance observer (FTDO) is employed. Using an FTDO, in a finite time interval, the disturbance parameters precisely can be identified which produce a better transient performance compared to the Lyapunov parameter estimation (LPE) method. Unlike previous literature, the imposed restrictions over external disturbances have been relaxed, i.e., the upper bounds of disturbances and the restrictive condition over the disturbances’ first derivatives have been removed. According to the proposed FTDO, a continuous control input is developed that eliminates chattering in synchronization of nonlinear MIMO master-slave system; as a result, a chattering-free TSMC is attained which makes the synchronization errors converge to the origin in finite-time period. By means of the Lyapunov function (CLF), the stability of the introduced TSMC and the FTDO are proved. Finally, in the simulation section, the efficiency and the accuracy of the proposed approach are revealed by applying the proposed method on a Chameleon master-slave chaotic flow.