Global finite-time stabilization of planar nonlinear systems by output feedback

This paper considers the problem of global finite-time stabilization by output feedback for a class of planar systems without controllable/observable linearization. The novelties of this work are: (1) we show that the adding a power integrator technique can be modified to construct a finite-time stabilizer for the planar systems; (2) a new nonsmooth one-dimensional observer is developed to estimate the unmeasurable state of the system; and (3) a rigorous stability analysis procedure is proposed to appropriately select the gain of the observer. The combination of the finite-time stabilizer and nonsmooth observer makes the planar system globally finite-time stable. We also show that as a direct application of the main result, global output feedback finite-time stabilization can be achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogenous.