Global finite-time stabilisation using bounded feedback for a class of non-linear systems

In this study, the authors consider the problem of global finite-time stabilisation for a class of non-linear systems by bounded feedback control. First, we use the generalised adding a power integrator and the nested saturation methods to design a saturated homogeneous state feedback controller. Under this bounded controller, a class of non-linear systems comprised of a chain of power integrators perturbed by uncertain bounded non-linearities can be globally stabilised in a finite time. Second, as an application of previous developed results, a bounded finite-time output feedback controller is designed for a class of special non-linear systems, which is comprised by a chain of integrators plus known bounded non-linearities. To estimate the unknown states in a finite time, a finite-time convergent observer is constructed. By substituting the estimated states into the state feedback stabiliser, it can be guaranteed that the closed-loop system is globally finite-time stable.