Observer Design For Descriptor Systems With Unknown Input And Measurement Noise

In this dissertation, design problems of observers for descriptor systems are considered. In order to satisfy the requirements of practical applications, we give a detailed discussion about design of observers with unknown input and measurement noise disturbances. The main contributions of this dissertation are as follows.For descriptor systems with unknown input disturbances, a new and easy approach is presented. Using this method, the full-order observers of linear descriptor systems with unknown input are obtained; the sufficient condition for the existence of the observers is given; and the analytical solution of this problem is addressed based on a group of indefinite matrix equations. Moreover, under some assumptions, we get a kind of proportional-integral(PI) observer; give a sufficient condition for the existence of the observer with proof; estimate the unknown input disturbances; and analyze the robustness of the observers about the uncertainty of parameters. Here, the two different forms, full-order and reduced-order, are developed.For non-square descriptor systems with measurement noises, we also design a kind of observer. By taking nonsingular transformation on the system, the problem about descriptor system is equivalently transformed into normal state space problem. At the same time,we give the sufficient condition for the existence of the observers and a simple design procedure. The observers asymptotically estimate both the state and the unknown input. Also, the analytical solution to the observer design problem is given.