Sampled-Data Stabilization of a Class of Nonlinear Systems With Application in Robotics

The output feedback stabilization problem for the class of nonlinear Lipschitz systems is considered. A discrete-time feedback controller is designed for the sampled-data case, where the output of the plant is only available at discrete points of time and where the objective is to stabilize the system continuously using a discrete-time controller. We show that exact stabilization in this case can be achieved using a direct sampled-data design approach, based on $H∞$ optimization theory, in which neither the plant model nor the controller need to be discretized a priori. The proposed design is solvable using commercially available software and is shown to have important advantages over the classical emulation approach that has been used to solve similar problems. The applicability of the proposed techniques in the robotics field is thoroughly discussed from both the modeling and design perspectives.