A unified approach to finite-time stabilization of high-order nonlinear systems with an asymmetric output constraint

The problem of finite-time stabilization for a class of high-order nonlinear systems (also known as p-normal form systems) with an asymmetric output constraint is investigated in this paper. A novel design approach is proposed by delicately revamping the technique of adding a power integrator with the introduction of a distinctive asymmetric barrier Lyapunov function and performing a skillful manipulation of sign functions. By using the present method, a continuous state feedback finite-time stabilizer can be recursively constructed while achieving the requirement of the asymmetric output constraint. The novelty of the proposed approach is that it is a unified manner that enables us to simultaneously tackle the problem of finite-time stabilization for high-order nonlinear systems with and without asymmetric output constraints, without changing the controller structure.