General scheme for design of higher-order sliding-mode controller

Higher-order sliding-mode control has exclusive properties, such as robustness against the disturbance and uncertainty. Moreover, the finite-time stability of a system can be realized with a homogeneous sliding-mode controller. However, designing a higher-order sliding-mode controller is difficult. In this paper, we introduce a general strategy that includes various types of homogeneous sliding-mode control laws. We can check the stability of a system under the control law with some explicit inequalities. Therefore, we can theoretically design the controller even if the target system has input constraints, bounded disturbances, and uncertainty.