Hybrid-Impulsive Second Order Sliding Mode Control: Lyapunov Approach

A perturbed nonlinear system of relative degree two controlled by discontinuous-impulsive feedbacks is studied. The hybrid-impulsive terms serve to drive instantaneously the system trajectories to the origin or to its small vicinity. In particular, impulsive-twisting control exhibits an uniform exact finite time convergence to the second order sliding mode (2-SMC) with zero convergence time. The stability of the considered hybrid-impulsive system is studied using Lyapunov approach.