An improved second-order sliding-mode control scheme robust against the measurement noise

In this note the second-order sliding-mode control problem is addressed and solved by explicitly taking into account the presence of measurement error with unknown upper bound δ. Under sensible assumptions regarding the uncertain dynamics of a broad class of nonlinear plants, a new switching controller is proposed guaranteeing a sliding accuracy of order O(τ²)+O(δ), τ being the sampling interval. Simulations highlight the effectiveness of the proposed approach and confirm the expected precision order.