The state feedback has shown its advantages in many synthetical problems, however, all state variables are rarely available from on-line measurement due to either the difficulties of measuring state directly or the economic and utilizing limitations of measuring equipment. This makes state feedback can not be physically realized under many conditions. The fact that the function of the state feedback can not be replaced and the physical realization for state feedback can not be reached makes up a kind of contradiction. One of the ways to solve this problem is to reconstruct the state variables of the system and to use it to replace the actual state variables of the system to satisfy the requirement of the state feedback. The state observer is both a theoretical and an applied subject developed under the background mentioned above. Because of the complexity of nonlinear systems, observer design method for nonlinear systems has not yet formed a complete system. Therefore, the problem of observer design of nonlinear systems is one of the hot issues.The present thesis focuses on the investigation of the observer design for nonlinear systems. For several different classes of nonlinear systems, we considered the observe designs for multi-input multi-output nonlinear systems and Lipschitz discrete-time nonlinear systems, and observer-based controller design for a class of discrete-time nonlinear systems respectively. The main research results are given as follows:The first, the problem of state observer design for a class of multi-input multi-output affine nonlinear systems is investigated. Based on input-output linearization method, a new approach of the state observer design for the multi-input multi-output affine nonlinear system is proposed. The sufficient conditions that guarantee the state observation error to converge to zero asymptotically are obtained. An example is given to show the validity of obtained results.The second, the observer design of the discrete-time nonlinear systems with nonlinear terms satisfying Lipschitz conditions is considered. Using Schur complement lemma and constructing Lyapunov function, three new sufficient conditions are given which guarantee the estimation error to asymptotically converge to zero. Observation gain matrices are obtained through solving a set of linear matrix inequalities. The effectiveness of this approach is validated with a simulation example.Finally, the problem of observer design for a class of discrete-time nonlinear systems is considered. Based on Schur lemma and Lyapunov stability theory, the approach of observer design for a class of discrete-time nonlinear systems is developed. Under appropriate conditions, it is proved that observer proposed assured that the observation error asymptotically converges to zero, Furthermore, the feedback design approach for a class of discrete-time nonlinear systems is considered based on the observer, and a sufficient condition is derived to ensure the stability of the considered system under the action of feedback control. |