Fixed-time stabilisation for a class of high-order non-linear systems

The problem of fixed-time stabilisation for a class of high-order non-linear systems is studied. By introducing the manipulation of sign functions and revamping by adding a power integrator technique, a novel approach is proposed to construct a continuous stabiliser as well as a continuously differentiable Lyapunov function, which is crucial for proving fixed-time stability. The novelty of this study is the development of a systematic design method that provides a delicate solution to the problem of fixed-time stabilisation for high-order non-linear systems.