Finite-Time Stability of MIMO Nonlinear Systems Based on Robust Adaptive Sliding Control: Methodology and Application to Stabilize Chaotic Motions

This paper introduces a robust adaptive sliding mode control to solve a finite-time stability of the uncertain nonlinear systems with multiple inputs and multiple outputs (MIMO). The proposed algorithm guarantees a strict robustness and fast convergence of the system trajectories to zero in a finite time under the negative effects of uncertainties and/or external disturbances. The fundamental methodology is based on an improved modification of the super-twisting sliding technique to alleviate an undesirable influence of the chattering phenomenon. In addition, a nonlinear adaptive law is constructed to ensure a strict stability of the control system even without prior awareness of the upper bounds of uncertainties and disturbances. A general stability of the closed-loop disturbed MIMO nonlinear system is achieved by the Lyapunov theorem. Lastly, the proposed algorithm is applied to stabilize the typical chaotic behaviors of Duffing - Holmes system and Lorenz system. The advantages and effectiveness of the proposed method are clearly demonstrated through the results of numerical simulations compared with other existent methods.