针对不确定系统测量输出矩阵含有不确定参数的问题,提出一种基于新龙伯格(Luenberger)类型观测器的鲁棒状态反馈设计方法.首先,针对实践中状态变量难以测量的问题,通过观测状态的反馈来进行观测器设计,考虑不确定系统中测量输出矩阵含有不确定参数的情况,设计一种新龙伯格类型观测器;其次,在新龙伯格类型观测器基础上,结合多仿射表示和松弛变量框架,得到与李亚普诺夫函数相关的凸线性矩阵不等式(LMI)条件,进而对闭环系统进行基于线性矩阵不等式组的鲁棒稳定性分析;最后,通过实验检验上述条件的可行性,证明该方法的实用性和有效性.

This paper proposes a robust state feedback design method based on a new Luenberger observer for uncertain systems with measurement output matrices containing uncertain parameters. First, in view of the problem that it is challenging to measure state variables in practice, an observer is designed through the feedback of the observation state. Considering the situation that the measurement output matrix contains uncertain parameters in the uncertain system, a new Luenberger observer is designed. Then, based on the new Luenberger observer, and combined with the multi-affine representation and the slack variable framework, the convex linear matrix inequality condition related to the Lyapunov function is obtained, and the robust stability analysis based on linear matrix inequalities is conducted for the closed-loop system. Finally, the feasibility of the above condition is tested by an experiment to show the applicability and effectiveness of the proposed method.