New approach to second‐order sliding mode control design

The second‐order sliding mode control generates important properties for closed‐loop systems, such as robustness, disturbance rejection and finite‐time convergence. In this study, it is shown that the adding a power technique plus the nested saturation method will bring in a new second‐order sliding mode control scheme for non‐linear systems with relative degree two. Based on this, a second‐order sliding mode controller is constructed by imposing a natural assumption on the sliding mode dynamics, that is, the uncertainty of the sliding mode dynamics can be bounded by a known function instead of a constant. Under the proposed sliding mode controller, it is proved that the closed‐loop system is not only globally convergent, but also locally finite‐time stable, which implies the global finite‐time stability. Finally, the effectiveness of the proposed method is verified by a numerical example.