Finite time stabilization of interconnected second order nonlinear systems

Finite time stabilization of interconnected second order nonlinear systems is addressed. Each subsystem is assumed to be weakly coupled through the inputs. To obtain finite time stabilization, a hybrid controller is used. Outside a ball centered at the desired position linear controller is designed to enter this ball, then, inside this ball, the controller switch to a discontinuous controller (in fact a second order sliding mode controller) in order to meet the desired time specification. Lastly, an application to the regulation of systems with coulomb friction is provided by the use of the proposed control strategy. The proposed algorithm is demonstrated with some simulations for a two-link manipulator.