A novel second-order sliding mode control based on the Lyapunov method

In this paper, a novel discontinuous second-order sliding mode control approach has been developed to handle sliding mode dynamics with a nonvanishing mismatched disturbance by using Lyapunov theory and a finite-time disturbance observer. Firstly, the finite-time disturbance observer is designed to estimate the nonvanishing mismatched disturbance. Secondly, a virtual controller has been constructed based on the estimated value such that the sliding variable can be stabilized to zero in a finite time. Then, the real discontinuous controller is designed to guarantee that the virtual controller can be well tracked in a finite time. Lyapunov analysis also verifies the finite-time stability of the closed-loop sliding mode control system. The developed discontinuous second-order sliding mode control method possesses two appealing features including strong robustness with respect to the matched and mismatched nonvanishing disturbances, and relaxation on the constant upper bound of uncertainties widely used in a conventional second-order sliding mode. Finally, an academic example is illustrated to verify the effectiveness of the proposed method.