High‐order sliding‐mode control design homogeneous in the bi‐limit

Abstract

Summary We provide a new Lyapunov‐based design of high‐order sliding‐mode (HOSM) controllers for a class of single‐input‐single‐output uncertain nonlinear systems. In contrast to the classical homogeneous HOSM controllers, the proposed design is based on approximating a system by homogeneous ones near the origin and far from it, that is, systems homogeneous in the bi‐limit, or bl ‐homogeneous systems, for short. Based on this idea, and using appropriate control Lyapunov functions, a family of bl ‐homogeneous HOSM controllers is designed. They are capable of establishing a sliding‐mode of arbitrary order in finite‐time. The proposed novel HOSM controllers improve robustness against persistently acting matched perturbations and enhance the convergence velocity of the controllers, allowing for fixed‐time convergence.