A finite-time sliding-mode controller design for convergence at a desired time and global robust control

This paper presents some further results on sliding mode control for a class of nonlinear systems with bounded uncertain parameters. A finite-time sliding manifold is proposed by incorporating piecewise defined function of time into the existing terminal sliding manifold, based on which a novel time-varying finite-time sliding mode controller is proposed. The proposed control strategy eliminates the reaching phase totally, and ensures the existence of a sliding mode throughout the entire response. On the other hand, it provides a means to predict the entire motion and the exact convergence time in advance, and an effective method is provided for the parameter selection to guarantee that the system states converge to equilibrium point at a desired time. Finally, simulation for a second-order system verifies the effectiveness of the proposed algorithm.