Practical stabilization of nonlinear systems in chained form

This paper presents a hybrid controller for the practical stabilization of general n-dimensional nonlinear systems in one-chained form. This controller consists of two parts: 1) a discrete-time part that practically stabilizes a subset of the system states; and 2) a piecewise continuous-time part that steers the remaining state-components to an arbitrarily small neighborhood of zero. One attractive feature of the proposed control approach is that it straightforwardly allows for generalizations in the sense that integrators can be put in cascade with the control inputs without affecting the closed-loop stability properties. This yields smoother control inputs, which makes the hybrid controller particularly useful for some relevant applications like mobile robots