Observer Design For A Class Of Nonlinear Delay Descriptor Systems

Descriptor system is a class of dynamic systems which is more general than any other systems. The theory of descriptor system has been developed sufficiently since1970s. Delay is a common phenomenon in engineering practice and the objective world. The study of delay systems generates many valuable results in recent years. Because of the generality of descriptor systems and the universality of delay phenomenon, we must also consider the impact of delays and singular phenomenon in many practical analysis systems to accurately describe them. In practice, because all state variables are available from on-line measurement works that are difficulty to measure state directly, which makes state feedback can not be physically realized. This requires us to observe the real state to satisfy the requirement of the state feedback. In practical problems, the real system usually can not be described by linear model, and it should be described by non-linear model. So observer design for nonlinear descriptor systems with time-delay has the theoretical significance and application value.This thesis focuses on the problems of observer sign for nonlinear descriptor systems with time-delay. The paper is summarized as follows:1. For descriptor systems with time-delay the full-order observer is designed. Firstly, the error equation system is changed into a neutral system, and then for this neutral system, Lyapunov stability approach makes it asymptotic stability and the criterion for the state observer is given.2. For a class of nonlinear descriptor systems with time-delay, full-dimensional observer is designed. Using the method of Lyapunov stability two results are got:when the external disturbance is zero, error equation is asymptotically stable and the concrete form of the system gain is given; when the external disturbance is not zero, H∞control condition for the system is met. For a class of nonlinear descriptor systems with time-varying delay, full-dimensional state observer is designed. Lyapunov stability approach makes the error equation asymptotic stability and the concrete form of the system gain is given.3. Observer design problem for a class of uncertain descriptor systems with constant delays is studied and the full-dimensional state observer of system is designed. Lyapunov stability approach makes the error equation asymptotic stability and the concrete form of the system gain is given.