Fixed-time stabilization of high-order nonlinear systems with an asymmetric output constraint

This article studies the problem of fixed-time stabilization for a class of uncertain high-order nonlinear systems subjected to an asymmetric output constraint. A tangent-type barrier function is first developed as an intermediate design ingredient by subtly extracting and utilizing the inherent features of system nonlinearities. Next, the proposed barrier function along with the intrinsic attributes of signum functions is exploited to elegantly renovate the celebrated technique of adding a power integrator, thereby establishing a unified approach by which a tangent-type asymmetric barrier Lyapunov function together with a continuous state feedback fixed-time stabilizer can be constructed systematically while guaranteeing the achievement of pre-specified output constraints successfully. A technical novelty of the presented scheme is ascribed to the unified nature enabling us to design a fixed-time stabilizer simultaneously workable for the system subjected to or free from output constraints without needing to revamp the controller structure. A numerical example is provided to show the effectiveness and superiority of the developed method.