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针对一类在有限时间下的线性奇异系统,同时考虑参数不确定性和有限外部扰动影响,研究了系统基于状态反馈控制器的鲁棒H∞控制问题。首先通过构造合适的Lypunov函数,利用线性矩阵不等式方法给出了线性广义系统有限时间有界且H∞范数有界的充分条件,在此基础上讨论线性广义系统的H∞状态反馈控制,给出了控制器存在的充分条件,同时给出了控制器的具体设计方法,控制器可由线性矩阵不等式解得。最后的数值算例说明了所提出方法的可行性和有效性。
For a class of linear singular systems with finite time, the robust H∞ control problem of the system based on state feedback controller is studied considering both the parameter uncertainty and the limited external disturbances. First, by constructing the appropriate Lypunov function and using the method of linear matrix inequalities, the sufficient conditions for the finite time boundedness and the bounded H∞ norm of a linear singular system are given. Then, the H∞ state feedback control for a linear singular system is discussed. The sufficient conditions for the existence of the controller are given. At the same time, the specific design method of the controller is given. The controller can be solved by the linear matrix inequality. The final numerical example illustrates the feasibility and effectiveness of the proposed method.