Improved Solvable Condition for H∞ Control Problem via State Feedback
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摘要: 考虑了状态反馈H∞控制可解条件的简化问题.状态反馈H∞控制问题的可解性可转化为一类线性矩阵不等式(LMI)的可解性,通过删除这类LMI中多余的矩阵变量,可减少矩阵变量的维数.而且,基于降维LMI的可行解,可构造出原LMI的可行解集.在此基础上,导出了简化的状态反馈H∞控制问题可解条件.基于简化条件的可行解,可构造出状态反馈H∞控制器簇,该控制器簇中含有丰富的自由参数.最后,给出了两个简单的例子,说明了文中方法的正确性.Abstract: Simplified solvable condition for H∞ control problem via state feedback is considered. The solvability of H∞ control problem via state feedback is considered to be equivalent to that of a class of linear matrix inequality (LMI). It can reduce the variable dimension by deleting redundancy matrix variables for the class of LMI, and a dimension-reduced LMI is obtained then. Moreover, the feasible solution set to the former LMI can be reconstructed via that of the latter. On the above basis, an improved solvable condition for H∞ control problem via state feedback is deduced. The H∞ controller set can be constructed by the feasible solution to the simplified solvable condition, and it also has more plentiful free parameters. Finally, two simple examples are given to show the validity of this approach.
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Key words:
- state feedback /
- linear systems /
- robust control /
- H∞ control /
- LMI
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