Observer Design And H_∞ Control For Descriptor Systems

Descriptor systems are a class of more general dynamic systems with extensive application background. So a great deal of interest has been devoted to the study of descriptor systems. The theory has been developed sufficiently since 1970s, and considerable results of normal systems were generalized to descriptor systems. In the light of recent work on the theory of descriptor systems, this thesis provides a systematic study on the problems of the observer design, the H_∞control, and robust control for descriptor systems. Some new design techniques are proposed. The main contents and results in this thesis are as follows:1. The problem of observer design for rectangular descriptor systems with unknown inputs is studied. The problem is equivalently converted into corresponding problem of normal state-space systems via simple algebraic transform. The sufficient condition for the existence of the observer and the designing method are given. The state and unknown inputs of descriptor systems are estimated using the state of the observer, control input and output of descriptor systems, and the estimations contain no the derivative. Furthermore, based on dynamic compensation, full-order observer design for rectangular descriptor systems is studied, and sufficient condition for the existence of the observer is given. The design procedure is also provided, which is simple and straightforward.2. An improved delay-dependent H_∞control problem for descriptor systems with time-delay is investigated. A new delay-dependent generalized bounded real lemma (GBRL) is presented in terms of a strict linear matrix inequality (LMI). Based on the GBRL obtained, a new delay-dependent condition for the existence of H_∞control via linear memory-less state feedback is presented by using matrix inequality. The condition fits a general descriptor system, i.e., whether the descriptor system with time-delay is impulse-free or not, and it is less conservative than existing ones.3. The problem of robust H_∞control for uncertain continuous descriptor systems with time-delay is addressed. Parametric uncertainty is assumed to be norm bounded. For all admissible parametric uncertainties, the observer-based controller is designed such that the resulting closed-loop system guarantees generalized quadratically stable with H_∞performanceγ. Besides, the conditions obtained have no equality constraint.