The thesis mainly deals with the fault tolerant control research project, which is one of challenging researches in control science. Under the support of a National Key Project, "System Reliability and Fault Tolerant Control" in the field of "Funda- mental Theory Research for Complex System", and based on functional redundancy fault tolerant control design method, fault tolerant control issues in complex control systems are discussed. The main work and contribution of this thesis are as follows: Firstly, the problem of designing a non-reconfigurable control system is con- sidered, so as to preserve stability for the closed loop control system when some functional redundancy actuator or sensor failure occurs, this is also the integrity problem of control system. Based on Riccati equation, Lyapunov stability principle and the generalized inverse theory, some fault-tolerant control system design meth- ods for linear multivariable continuous-time system with actuator or sensor failure are presented. Then some sufl:icient conditions are obtained for the existence of the robust fault-tolerant controller, which has both integrity to actuator or sensor fail- ure and closed pole restriction. According to the proposed design method, the state feedback controller sets all closed-loop poles within a prescribed circular region. It not only retains asymptotic stability in the case of sensor or actuator failure, but also has robust stability to parameter perturbation. Secondly, based on the generalized inverse theory and active fault tolerant control ideology, a design approach that using multiple controllers and switching strategy for linear continuous-time system is proposed. The state-feedback system has good dynamic characteristics to actuator failure because the closed-loop poles are placed in a specified circular region. This method automatically detects and identifies the failed component and reconfigures control action. Through switching, the fault tolerant control system not only guarantees the system stability, but also has good performance in the case of actuator failure during operation. Thirdly, the problem of setting all poles of a closed-loop system in a specified disk by state feedback is analyzed for discrete multiple time delay systems. Some sufficient conditions are firstly given to guarantee the D stability for discrete multiple time delay systems. Then, several new robust D-stability criteria are put forward to guarantee the robust D stability for discrete multiple time delay systems with both unstructured and highly structured parametric perturbations. Fourthly, based on linear matrix inequalities (LMI) technique, a fault tolerant controller design method with pole constraints is proposed. For both continuous time and discrete time systems, a design frame for D stable fault-tolerant controller in the case of actuator failure is given. A sufficient condition on the existence of proposed fau
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