Robust Fault Tolerant Control For Delta Operator Formualted Uncertain Systems With Time-delay

With large-scale and complex development, it is very important signification to ensure the reliability and the security of modern systems. The fault-tolerant control (FTC) provides a new method to improve the reliability of modern complex systems as a new subject. Due to transferable delays, time-delay is inevitable in actual systems. But time delays is a major cause of performance degradation, it may lead to loss of stability. Therefore, study on FTC of time-delay systems with uncertainty is more suitable for reality. Moreover, as a unified method of the cotinous-time systems and discrete-time systems, delta operator can conquer the numerical instability problems caused by the conventional shift operator while the sampling rates increased. The thesis is supported by Natural Science Foudation of Henan Province entitled "Fault detection and fault tolerant control for delta operator formulated systems with time-delay". The main contributions are as follows:(1) The problem of fault tolerant control for delta operator time-delay uncertain systems with regional pole constraints is considered. Sufficient conditions of robust D-stability for delta operator formulated fault tolerant control systems with state delay are presented in terms of Lyapunov-Krasovskii stability theory and linear matrix inequality (LMI) approach. When this LMI is feasible, the parameterized representation of the desired state feedback controller is also obtained. A numerical simulation shows the effectiveness of the proposed method.(2) The problem of delay-dependent robust fault-tolerant control for delta operator formulated uncertain systems with time-varying delays and regional pole assignment constraints are studied. Based on Lyapunov stability theory and linear matrix inequality approach, a sufficient condition of delay-dependent robust fault-tolerant D-stabilization for delta operator systems with time-delay and actuator failure is provided. When LMI is feasible, the state feedback control law of the delay-dependent systems is also obtained. A numerical simulation shows the advantages of delta operator approach and the effectiveness of the proposed method.(3) The H∞reliable control problem is studied for delta operator formulated uncertain systems with time-delay. The continous model of actuator failure and sensor failure is considered, a sufficient condition for the existence of the H∞reliable controller is derived via the LMI approach, and a design procedure of the controllers is presented. The design method of such controller not only guarantees asymptotic stability of uncertain time-delay systems, but also satisfies H∞performance index. A numerical example is provided to demonstrate feasibility and efficiency of the method.