A unified approach to finite-time stabilization of high-order nonlinear systems with and without an output constraint

This paper considers the problem of state feedback finite-time stabilization for a class of high-order nonlinear systems with an output constraint. By proposing a novel tan-type barrier Lyapunov function combined with manipulating sign functions, the technique of adding a power integrator is skillfully revamped to develop a systematic approach that guides us to construct a state feedback finite-time stabilizer for high-order nonlinear systems while preventing the violation of a prespecified output constraint during operation. The proposed approach is a unified tool in the sense that it can provide a finite-time stabilizer design even when the constraint is infinite, or equivalently, there is no need for a constraint. A simple example is presented to demonstrate the effectiveness of the proposed strategy.