一类不确定离散奇异系统的鲁棒稳定化

Robust stabilization for a class of discrete-time singular systems with uncertainties

讨论了离散奇异系统矩阵E中含时不变参数不确定的鲁棒状态反馈稳定化问题.首先,在一系列等价变换下,阐述了其和一个不确定正常线性离散系统的鲁棒状态反馈稳定化问题的等价关系;然后,利用线性矩阵不等式(LMI)方法,给出了鲁棒状态反馈稳定化控制器存在的一个充分必要条件,控制器的设计方法及控制器的一个解;最后,通过一个数值算例验证了本设计方法的有效性.

The robust stabilization via state feedback for discrete-time singular systems with norm-bounded time-invariant parameter uncertainties in the matrix E is discussed.In a series of equivalent transformation,the equivalence between the stabilization under discussion and the robust stabilization via state feedback for uncertain standard state-space discrete-time linear systems was obtained.In terms of linear matrix inequality(LMI),a necessary and sufficient condition where there exists a robust state feedback stabilizing controller was (given).The design method of the controller and a solution of the controller were also given.The effectiveness of the proposed method was illustrated through an example.