Controller and observer design for a class of nonlinear systems

This paper considers the full-state feedback control problem,the observer design problem and the output feedback control problem for a class of nonlinear systems.First,a linear full-state feedback controller is designed and a sufficient condition is derived,under which the exponential stabilization is achieved.Second,a nonlinear observer is proposed and it is shown to be an exponentially stable observer.Furthermore,given that the sufficient conditions of the controller and observer problem are satisfied,it is shown that the proposed controller with estimated state feedback from the proposed observer will achieve the exponential stabilization.Finally,a simulation example is given to verify the effectiveness of the obtained results.