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针对状态具有多个时滞的线性连续系统,基于Lyapunov稳定性理论和线性矩阵不等式方法(LMI),采用无时滞记忆的状态反馈控制律,研究了在执行器发生故障的情况下,连续多时滞系统的最优H_∞容错控制问题。首先,给出了系统没有干扰输入时存在无记忆状态反馈容错控制器的一个充分条件;进一步,给出了在H_∞扰动衰减指标约束下,系统存在无记忆状态反馈H_∞容错控制器的一个充分条件;最后,给出了最优无时滞记忆状态反馈H_∞容错控制器的设计方法。仿真实例证明了所得最优H_∞容错控制器设计方法的正确性和有效性。
Aiming at the linear continuous systems with multiple delays in state, the state feedback control law without time-lapse memory is used based on Lyapunov stability theory and linear matrix inequality method (LMI) Optimal H_∞ Fault Tolerant Control of Hysteresis System. First, a sufficient condition for a fault-tolerant controller with no memory state is given when there is no disturbance in the system. Furthermore, a H_∞ fault-tolerant controller with memoryless state feedback is given under the constraint of H_∞ disturbance attenuation index Sufficient conditions. Finally, the design method of optimal H_∞ fault-tolerant controller with time-delay memory state feedback is given. The simulation example proves the correctness and validity of the design method of the optimal H_∞ fault-tolerant controller.