Observer Design For A Class Of Nonlinear Descriptor Systems

It is well known that the descriptor system has higher capability to describe a physical system. Descriptor system models are more convenient and natural than normal models such as power systems, economic systems, robot systems, electrical network analysis and so on. This is the reason why descriptor system problems have attracted much interest of many scholars in recent years. There have been a lot of achievements on the stability, controllability and observerability. The state feedback has shown its advantages in many descriptor system problems. The pole assignment, stabilization and linear quadratic optimal control of the descriptor systems all depend on introducing some proper state feedback to the systems. In practice, however, all state variables are rarely available from on-line measurement due to the difficulties of measuring state directly, which makes state feedback can not be physically realized. This makes us observe the real state to satisfy the requirement of the state feedback. The state observer of descriptor systems is both a theoretical and an applied subject developed under the background mentioned above.Over the last decades, tremendous research activities have focused on observer design for descriptor systems. The state estimation of descriptor system can be used for control, diagnosis or supervision of descriptor systems, such as power systems, economic systems, robot systems and electrical network analysis. Meanwhile we also can make use of the observer state to finish state feedback and achieve additional performances and specifications.This thesis focuses on the problems of observer design for nonlinear descriptor systems and is organized as follows:The design problem of full-order and reduced-order observers for a class of nonlinear descriptor systems is considered. Using the differential mean value theorem (DMVT), we transform the nonlinear error dynamics descriptor systems into a linear parameter varying (LPV) descriptor system. If the given linear matrix inequalities (LMIs) are feasible, there exists a full-order observer and the existence of a reduced-order observer is also guaranteed. The stability of the error system is analyzed by a Lyapunov function, which shows that the errors are exponential convergent. Finally, simulation results show that the obtained method is valid and better than existing results.The observer design problem of nonlinear generalized proportional integral (NGPI) and nonlinear generalized proportional integral derivative (NGPID) for a class of nonlinear descriptor systems is considered. NGPI observers and NGPID observers are proposed. Using the differential mean value theorem (DMVT), we transform the nonlinear error dynamics descriptor system into a linear parameter varying (LPV) descriptor system. Then the stability of the error system is analyzed by a Lyapunov function and convexity principle, which shows that the errors are exponential convergent. If the given linear matrix inequalities (LMIs) are feasible, all the matrix gains can be obtained easily. The new design method can offer more degrees of design freedom, by which a more comprehensive type of nonlinear descriptor systems can be designed. Finally, simulation results show that the obtained method is valid and better than some existing results.