Output feedback finite-time stabilization for high-order planar systems with an output constraint

This paper investigates the problem of output feedback finite-time stabilization for a class of high-order planar systems with an output constraint. By developing a nonsmooth observer and revamping the technique of adding a power integrator with the introduction of a new tan-type barrier Lyapunov function as well as a skillful manipulation of sign functions, a continuous finite-time output feedback stabilizer is explicitly constructed while achieving the requirement of the output constraint. The novelty of the proposed scheme lies in the unified design that is able to simultaneously perform the output feedback finite-time stabilization for systems with and without output constraints, without the need of changing the controller structure.