圆形极点区和状态方差上界约束下H_∞指标的优化

Optimization of H_∞ Index under Constraints of Circular Pole and State-variance Upper Bound

该文对一类随机状态反馈系统 ,利用线性矩阵不等式 (LMI)方法 ,分析了闭环系统的、与约束圆形极点区相容的状态方差上界指标 ,得到了相容状态方差上界指标的较好取值范围 ,进而研究了相容极点区域与状态方差上界约束下 ,系统被控输出对扰动输入的H∞ 抑制界优化问题 ,给出了次优H∞ 抑制界和相应约束次优H∞ 控制。利用算例对所得结果作了说明。

For a class of stochastic state feedback systems, the state variance upper bound index consistent with pre specified circular pole index is discussed via linear matrix inequality (LMI) approach, a good range is given for variance upper bound index consistent with pre specified pole index. The optimization of H infinite attenuation index from disturbance input to controlled output is studied for the considered systems under constraints of consistent pole index and variance upper bound index. A sub optimal value of H infinite index is obtained via LMI approach and a method to find the constrained sub optimal control is provided. Finally, the obtained results are illustrated by a numerical example.