Controller Design for Second-Order Sliding Mode Dynamics with an Upper-Triangular Perturbation

This paper has investigated the second-order sliding mode (SOSM) controller design problem for a class of sliding mode dynamics with an upper-triangular perturbation. The construction of this SOSM controller consists of two steps. The first step is to use the adding a power integrator technique to construct a Lyapunov-based controller which locally finite-time stabilizes the sliding variables. The other step is to impose a kind of nested saturation function on the Lyapunov-based controller and adjust the saturation level to ensure the global convergence of sliding variables. Lyapunov analysis has been utilized to test the finite-time stability of the closed-loop system. Simulation results are given to verify the effectiveness of the proposed method.