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针对状态和控制输入同时具有多个时滞的线性离散时间系统,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,研究了执行器故障情况下,离散多时滞系统的H_∞容错控制问题。在采用连续执行器故障模型条件下,给出了系统没有干扰输入时存在无时滞记忆的状态反馈容错控制器的充分条件;进一步,给出了在H_∞扰动衰减指标约束下,系统存在无时滞记忆的状态反馈H_∞容错控制器的充分条件,并将结论推广到离散故障模型的情况。仿真结果证明了所提H_∞容错控制器设计方法的正确性和有效性。
Aiming at the linear discrete time system with multiple delays in state and control inputs, a state feedback control law without time-delay memory is proposed based on Lyapunov stability theory and linear matrix inequality method (LMI). In the case of actuator failure, H_∞ Fault Tolerant Control Problem for Discrete Systems with Multiple Time Delays. Under the condition of using continuous actuator fault model, the sufficient condition of state feedback fault-tolerant controller with time-delay memory without disturbance input is given. Furthermore, under the constraint of H_∞ disturbance attenuation index, The sufficient condition of H_∞ fault-tolerant controller with state feedback of time-delay memory is extended and the conclusion is generalized to discrete-time fault model. The simulation results prove the correctness and effectiveness of the proposed H_∞ fault-tolerant controller design method.