Controller and observer design for Lipschitz nonlinear systems

We consider three related problems for stabilization of a class of Lipschitz nonlinear systems: (1) full-state feedback controller design, (2) observer design, and (3) output feedback controller design. Sufficient conditions are developed for the design of an exponentially stable linear full-state feedback controller and an exponentially stable nonlinear observer. Given that the sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimated state feedback from the proposed observer will achieve exponential stabilization. Simulation results on an example are given to numerically verify the proposed designs.