Study On Several Problems Of Robust Control For Uncertain Singular Systems

It is well known that the design of control system is established based on the exact mathematical mode of plant, it is difficult to obtain its exact model in general such that the system uncertainties which include parameter uncertainties, un-modeled dynamics, and disturbances should be taken into account for modeling. The robust control theory mainly focuses on the study of how to design an admissible controller for a given uncertain system such that the resulting closed-loop system is stable with some specified system performance measures. Singular system is a kind of dynamical systems of more general and has been widely applied. Many physical systems are described more convenient and natural by singular system. Recently, a lot of research efforts have been drawn on the study of singular systems, and many results of normal systems have been corresponding generalized to singular systems.The robust control problem for uncertain singular systems is studied in this dissertation. Based on the linear matrix inequality (LMI) theory, the problems of robust passive control, robust H_∞control and robust variable structure control are studied. The main contents of this dissertation are outlined as follows.(1) The robust strictly passive control of continuous- and discrete-time linear singular systems with norm-bounded uncertainties is developed. Sufficient and necessary conditions, which ensure that the system is admissible and strictly passive, are established. A robust state-feedback controller and an unbias filter are designed for continuous-time singular systems and a robust static output-feedback controller is developed for discrete-time singular systems and the constraint matrix is transformed into a strict linear matrix inequality by using the matrix orthogonal complement.(2) Based on a integral inequality method, a new delay-dependent sufficient condition is presented for continuous singular system with variable time delay and norm-bounded uncertainties in terms of strict linear matrix inequalities, which guarantees that the system is robust regular, implusive-free, stable and strictly passive. Based on this sufficient condition, the robust strictly passive control problem is investigated. Compared with the previous methods, the proposed method is shown to be less conservative and involves no decomposition of system matrices.(3) Based on a finite sum inequality for quadratic terms, a new delay-dependent sufficient condition is presented for discrete singular system with variable time delay in terms of strict linear matrix inequalities, which guarantees the system to be robust regular, causal, stable and with an H_∞performance. Contrasted to the previous method, the proposed method involves no decomposition of system matrices. Based on this sufficient condition, the discrete robust H_∞controller is correspondingly given by using a descriptor mode method, which involves no nonlinear problem.(4) The variable structure control problem is studied for a class of singular systems with unmatched uncertainties in state matrix and for a class of normal time-delay state space systems with unmatched uncertainties both in state matrix and control gain matrix. And the corresponding switched surfaces and variable structure control laws are given respectively.