Designing a control system needs looking for exact mathematical mode of plant, but the mode can not be obtained in any case.. Therefore, the model may contain the uncertainties such as parameter uncertainties, un-modeled dynamics, external disturbances and so on. The robust control theory studies on the uncertainties model, which makes a closed-cloop system stable and satisfies some specified performance. Singular system is a kind of general dynamical system, and many systems are described more simple and natural by singular system. Recently, increasing attention has been paid to the studies of singular systems, some solutions of general systems have been generalized, but now, its research needs deep development. Reduce-order control theory is widely used in industry , military , aviation, spaceflight and so on, which catches great automation, and it has been an important branch of automation.In the dissertation, the uncertain discrete singular system is studied by linear matrix inequations (LMI), and is studied the robust performance by reduced-order control.Firstly, a guaranteed cost non-fragile robust controller is designed for an uncertain discrete singular system. The constraint inequation is transformed into a strict linear inequality by using two equalities; the controller and the guaranteed cost upper bound are given based on the solutions of the linear matrix inequality. And the approaches of designing the controller are given in terms of linear matrix inequalities.Secondly, a non-fragile Reliable robust controller is designed for an uncertainties discrete singular system with the D-stability, which makes the singular system to be regular, causal and D-stable with the parameter uncertainties changing and the actuator failures. The constraint inequation is transformed into a strict linear inequality by using two equalities, and the results to be obtained the controller are given by LMI.Thirdly, for the first time, the non-fragile control theory with covariance constraint is proposed for a discrete singular system. The exist condition of controller is given based on robust control theory. The state feedback controller and the covariance upper bounds can be given by the solutions of LMI, which makes the system satisfy a covariance constrain theory, and the results are given by LMI.At last, based on Luenberger observer, a reduced-order H_âˆžnon-friagile controller of a discrete system is studied for discrete system. The reduced-order observer is designed to make the error between the output of the controller and the input of the state feedback to zero. The input of the discrete system is the output of the observer to make the closed loop system satisfy the Hâˆžcondition, and the results are given by LMI... |