Output feedback control of second-order systems via Lipschitz continuous sliding modes

This paper presents an output feedback approach for second-order systems with non-vanishing perturbations. The proposed approach allows us to compensate for non-vanishing Lipschitz perturbations theoretically exactly while generating a Lipschitz continuous control signal, reducing the energy consumption by the control. To achieve such a Lipschitz continuous sliding mode control, we propose a homogeneous third-order sliding mode control law and a second-order sliding mode observer; then, we prove the finite-time stable equilibrium in a closed loop with the system. The feasibility of the result is shown through a simulation example.