Hybrid‐impulsive second‐order sliding mode control: Lyapunov approach

Dynamic system of relative degree two controlled by discontinuous‐hybrid‐impulsive feedback in the presence of bounded perturbations is considered. The state feedback impulsive‐twisting control exhibits a uniform exact finite time convergence to the second‐order sliding mode with zero convergence time. The output feedback discontinuous control augmented by a simplified hybrid‐impulsive functions provides uniform exact convergence with zero convergence time of the system's states to a real second‐order sliding mode in the presence of bounded perturbations. Only ‘snap’ knowledge of the output derivative, that is, the knowledge of the output derivative in isolated time instants, is required. The output feedback hybrid‐impulsive control with practically implemented impulsive actions asymptotically drives the system's states to the origin. The Lyapunov analysis of the considered hybrid‐impulsive‐discontinuous system proves the system's stability. The efficacy of the proposed control technique is illustrated via computer simulations. Copyright © 2016 John Wiley & Sons, Ltd.