摘要
介绍了线性矩阵不等式的基本概念和用于求解线性矩阵不等式的软件工具箱Matlablmi的3个求解器,对线性矩阵不等式在控制系统中的应用作了详细的综述。分析了其在当前的两个研究热点,即不确定系统的鲁棒控制与鲁棒滤波中的运用。同时探讨了时滞系统与非线性系统的研究现状。然后列举了一些具有代表性的采用LMI求解控制问题的最新结果。为了说明线性矩阵不等式的求解过程,给出了一个保性能控制的例子,在Matlab5 3编辑器中运行程序,得到的结果是最优性能指标值,copt=J 10 6777。
Some basic concepts about Linear Matrix Inequalities (LMIs) were introduced. Three solvers of LMI toolbox of the software Matlab were also presented. A review on the theory and application research for LMI in control systems was described in detail, mainly including robust control and robust filtering of uncertain systems. At the same time, some nonlinear systems and timedelay systems were discussed. And then, a list of new results of some representative control problems via the LMI approach were introduced. Finally, an example was presented to illustrate the procedure of solving LMIs,the programme is processed in the Matlab 5\^3 editor.The derived result is optimization in the state and copt=J\+*10\^677?7.
出处
《控制工程》
CSCD
2003年第2期145-148,189,共5页
Control Engineering of China
关键词
线性矩阵不等式
控制工程
时滞系统
鲁棒控制
linear matrix inequality
time-delay, convex optimization
LMI toolbox
