Output feedback hybrid-impulsive second order sliding mode control: Lyapunov approach

A perturbed nonlinear system of relative degree two controlled by output feedbacks discontinuous-hybrid-impulsive control is studied. The output hybrid-impulsive terms serve to drive instantaneously the system´s trajectory to the origin or to its small vicinity. The output feedback impulsive action combined with the output relay feedback control guarantees a uniform exact convergence with zero convergence time of system´s trajectory to a real 2-SMC in the presence of bounded perturbations. The stability of the considered hybrid-impulsive system is studied using Lyapunov approach.