Research Of Correlative Theory On Fault-tolerant Control For Descriptor Systems

Modern systems are developing towards larger and more complicated scale. Vast loss of wealth and lives is caused if systems failures occur in this kind of control systems. It is important to improve reliability and safety of systems. Fault-tolerant control pioneers a new way to enhance the reliability of complicated systems. Fault-tolerant control for descriptor systems is not only a reasonable extension to control for normal systems but also a practical demand for descriptor systems, which have abundant applied backgrounds. So it is of important theoretical and practical engineering meaning to study the fault-tolerant control for descriptor systems.In this paper, a detailed analysis of the current situation of study on fault-tolerant control for descriptor systems and a discussion about the problems of fault-tolerant for descriptor systems are stressed. This paper includes integrity of fault-tolerant control for descriptor linear systems, observer-based active fault-tolerant control for descriptor linear systems and a class of fault-tolerant control for uncertain descriptor systems. The main results in this paper can be given as the following.On the passive fault-tolerant control for descriptor systems, its hot issue----the integrity of fault-tolerant control is researched by considering the design of circular regional controller with integrity for descriptor linear systems. Firstly, based on linear matrix inequalities (LMIs) , a sufficient and necessary condition of circular regional controller possessing integrity for descriptor linear systems is given. Furthermore, against the case of actuator and sensor failures, the above LMIs are appropriately amended. Then the circular regional controller possessing integrity for descriptor systems is obtained.On the active fault-tolerant control for descriptor systems, the problem of observer-based active fault-tolerant control for descriptor linear systems is considered. A method of designing observer-based active fault-tolerant control against sensor failures for descriptor linear systems is proposed. Based on separation theory for descriptor systems, when the sensor failure, simply re-designed state observer, and the controllers remained unchanged. Namely, control systems can tolerate sensor failure by adjusting the parameters of observer gain matrix.The design problem of fault-tolerant controllers for a class of uncertain descriptor systems is discussed in the normal conditions as well as in the event of sensor or actuator failures. A method of designing fault-tolerant controllers possessing integrity for a class of uncertain descriptor systems is presented. First, the state feedback controllers are designed using LMIs such that the well working order descriptor systems are asymptotical stabilization. Then the state feedback controllers are derived such that the resulting closed-loop descriptor systems are asymptotically stable when actuator failure occurs in descriptor systems. Further the fault-tolerant controllers possessing integrity under state feedback are presented using LMI method. Meanwhile the design approach of fault-tolerant controllers with integrity under output feedback is also obtained when sensor fault occurs. As can be seen from the design, the design problem of fault-tolerant controllers possessing integrity for a class of uncertain descriptor systems has been solved in LMIs.