Global finite-time controller design for HOSM dynamics subject to upper-triangular structure

In this paper, a novel saturation-based control method is proposed for high-order sliding mode (HOSM) dynamics with upper-triangular nonlinearities. Firstly, a new HOSM dynamics with upper-triangular nonlinearities is constructed based on the traditional HOSM dynamics, so as to reduce the uncertainties in the control input channel. Then, a HOSM controller is established by means of the adding a power integrator method such that the new HOSM dynamics is locally stabilized. Finally, the saturation-based controller is constructed by a combination of the saturation technique and the local HOSM controller to guarantee that the sliding variables can converge into a domain of attraction in a finite time and retain inside it thereafter. The rigorous stability analysis is made by the Lyapunov theory. A simulation example is also given to demonstrate the effectiveness of the proposed method.