Time-Varying Second-Order Sliding Mode Control for Systems Subject to External Disturbance

In this article, the design problem of a class of novel second-order sliding mode controller for systems subject to external disturbance is investigated, where the sliding variable is affected by a time-varying regulation. On the one hand, for the unmatched disturbance bounded by positive functions, a second-order sliding mode controller is proposed to prove the finite-time stability of aforementioned system through the backstepping-like method and virtual control strategy. On the other hand, for the non-vanishing bounded disturbance, a non-singular terminal sliding mode surface containing disturbance observations is designed via a finite-time disturbance observation method and the finite-time stability of the system controlled output is realized. The claimed performances of the proposed methods are validated by two simulation examples.