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针对一类具有外部扰动输入的不确定奇异周期系统,研究了该类系统的鲁棒容错H∞控制的问题,其中不确定性存在于系统的状态矩阵和输入矩阵当中,且满足范数有界条件。利用线性矩阵不等式(LMI)和李雅普诺夫不等式的分析方法提出了不确定奇异周期系统的鲁棒二次稳定和鲁棒二次可镇定且具有H∞性能指标的概念,得到了该类系统鲁棒容错H∞控制的充分和必要条件,并给出了系统状态反馈鲁棒容错H∞控制器的设计方法,所设计的H∞控制器既保证了闭环系统对故障发生时的鲁棒性,又能保证系统满足一定的H∞性能γ。研究成果是不确定奇异定常系统鲁棒容错H∞控制结论向不确定奇异周期系统的推广,因而具有较大的理论意义。最后,文章给出的数值算例证明了结论的有效性。
For a class of uncertain singular periodic systems with external perturbation inputs, the robust fault-tolerant H∞ control problem for such systems is studied. Among them, the uncertainties exist in the state matrix and the input matrix of the system, condition. The concepts of robust quadratic stability and robust quadratic stabilization with H∞ performance index for uncertain singular periodic systems are proposed by means of linear matrix inequality (LMI) and Lyapunov inequality analysis. The sufficient and necessary conditions for the fault-tolerant H∞ control of the rod are given, and the design method of robust fault-tolerant H∞ controller for the state feedback of the system is given. The designed H∞ controller not only guarantees the robustness of the closed- But also to ensure the system to meet certain H∞ performance γ. The research result is the extension of the conclusion that the robust fault-tolerant H∞ control for uncertain singular stationary systems to the singularly periodic systems of uncertainties has great theoretical significance. Finally, numerical examples given in the paper prove the validity of the conclusion.