  The stabilization of nonlinear systems under zero-state-detectability
assumption or its analogues is considered. The proposed supervisory control
provides a finite time practical stabilization of output and it is based on
uniting local and global controllers. The global control ensures boundedness of
solutions and output convergence to zero, while local one ensures finite time
convergence to a predefined set into the zero dynamics set. Computer simulation
illustrates advantages of the proposed algorithm.
