Controller Design for High-Order Sliding Mode Dynamics with Upper-Triangular Uncertainties

This paper is concerned with controller design for high-order sliding mode (HOSM) dynamics with upper-triangular uncertainties. First, we design an HOSM controller by means of the adding a power integrator method in order to locally stabilize the HOSM dynamics with upper-triangular uncertainties. On this basis, by combining the saturated technique and the local HOSM controller together, we devise a saturated-like controller in order to ensure the finite-time convergence of the sliding variables into a domain of attraction without an escape from the domain thenceforth. The stability results are established based on the Lyapunov theory. The efficiency of the designed saturated-like HOSM controller is validated by a numerical example.