Robust Fault-tolerant Control For Uncertain Linear Time-delay Systems

The reliability of systems is the key to operate normally for the systems. It has very important signification to ensure the reliability and the security of modern complex systems. The coming of the fault-tolerant control and fault-diagnosis provides a new method to improve the reliability of modern complex systems. Because of the abundant applied background of uncertainty and time-delay in practice and the complexity of analysis and synthesis, the study of the robust fault-tolerant control problem of uncertain time-delay systems has an important value in theory and in practice.Due to the safety of large-scale complicated control systems, uncertain linear time-delay continuous or discrete systems are respectively considered as control subjects in this paper. Based on Lyapunov stability theory, D-stability theory, vector inequality, memoryless state feedback control, time-delay state feedback control and linear matrix inequality method, the robust fault-tolerant control problems are studied in my work. There are main aspects in the work as follows:(1) The robust fault-tolerant control problem is studied for a class of uncertain linear time-delay continuous systems. Based on the linear matrix inequality method and Lyapunov stability theory, the sufficient conditions for the closed loop systems against actuator failures possessing robust fault-tolerant ability are given by respectively adopting memoryless state feedback laws and time-delay state feedback controller (where state feedback constant does not necessarily equal to time-delay constants of system). Controller parameters are calculated by using LMI toolbox in Matlab. The results of simulation demonstrate the effectiveness and feasibility of the presented method.(2) The robust fault-tolerant control problem is studied for a class of uncertain linear time-delay discrete systems. Based on the linear matrix inequality method and Lyapunov stability theory, the sufficient conditions for the closed loop systems against actuator or sensor failures possessing robust fault-tolerant ability are given by respectively adopting memory state feedback controller (where state feedback constant does not necessarily equal to time-delay constant of system). Controller parameters are calculated by using LMI toolbox in Matlab. The results of simulation demonstrate the effectiveness and feasibility of the presented method.(3) The robust D-stability fault-tolerant control problem is studied for a class of uncertain linear time-delay discrete systems. Based on the D-stability theory and linear matrix inequality method, the sufficient conditions for the closed loop systems against actuator or sensor failures possessing robust D-stability fault-tolerant ability are given by respectively adopting time-delay state feedback controller. Controller parameters are calculated by using LMI toolbox in Matlab. The results of simulation demonstrate the effectiveness and feasibility of the presented method.