Observer Design For Descriptor Systems

In this dissertation, design problems of observers for descriptor systems are considered and discussed detailedly. The two main contributions in this dissertation are as follows.Firstly, for linear descriptor systems with measurement output noises and input disturbances, a new descriptor observer technique is developed. The necessary and sufficient condition for existence of the present observer is derived, and a systematic design approach is addressed. The effect of uncertainties is decoupled completely, and the asymptotic estimates of the descriptor system state and the output noise are obtained simultaneously. And, the Luenberger estimator is also given. Secondly, for a class of nonlinear descriptor systems with both output noises and input uncertainties, a nonlinear descriptor estimator is derived by using the proposed approach, together with the linear matrix inequality technique. The existence and convergence of the nonlinear descriptor estimator is proven. The asymptotic estimates of the descriptor system state and the output noise are obtained at the same time. And, the present two estimators are applied to the sensor fault diagnosis, and hence the sensor fault can be estimated asymptotically. Numerical examples are included to illustrate the proposed design procedures and applications. Simulation results show good estimating performance. Finally, for descriptor systems with different input disturbances and measurement noises, we get a new observer method, and give a discussion about the effect of the noises to the error.The above approach is applied to normal systems with measurement noises. We present PD and PID descriptor observers, and give the physical meanings of the gain parameters. The applications of the proposed observers for systems with actuator and sensor faults are also discussed. Numerical examples are also given to illustrate the design procedures, and the simulation results show the satisfactory tracking performance. In a word, we give a unified approach of observer design about descriptor linear systems and nonlinear systems with Lipschitz constraint, as well as normal systems , all of which having unknown inputs.