基于极点与输出方差约束相容性分析的状态反馈

State Feedback Based on Consistency Analysis of Pole and Output-Variance Constraints

研究一类线性随机系统的满意状态反馈 ,期望闭环系统同时满足给定的圆形极点与输出方差约束 .先分析这两类约束指标的相容性 ,利用线性矩阵不等式 (LMI)方法 ,给出与极点指标相容的输出方差上界 (或下界 )指标的较好取值范围 .然后 ,对具有相容极点与输出方差指标的控制问题 ,给出设计理论 ,特别对输出方差指标是区间的情形提出一种控制设计方法 .算例对所得结果及所提设计方法作了说明 .

This paper studies satisfactory state feedback control for a class of linear stochastic systems so that resulting closed loop systems satisfy pre specified circular pole and output variance constraints simultaneously. The consistency of constraint indices for output variance and pole is analyzed first. By means of linear matrix inequality (LMI) approach, a good range is presented for output variance upper bound (and lower bound) index that is consistent to a given pole index. Then a control design theory is proposed for considered systems with consistent circular pole index and upper bound index of output variance, furthermore, a control design technique is provided as the output variance index is specified in terms of a certain region. Finally an example is given to illustrate the results obtained and the design scheme provided.