状态反馈中圆形极点与状态方差约束的相容性

摘要

The consistency of constraint indices of state variance and circular pole is studied for a class of stochastic systems with state feedback control.Two necessary and sufficient conditions are given, in terms of linear matrix inequalities(LMIs), for the existence of state feedback control with circular pole constraints.Satisfactory control design methods are provided for state feedback control with constraints of circular pole and consistent state-variance.By finding the maximum and minimum of matrix trace subject to LMIs，a good range is presented for all steady state-variance which is consistent with the given regional pole.Finally, an example illustrates that obtained results in this paper are of simplicity and validity.%对一类线性随机系统的状态反馈问题，研究了两类约束指标：状态方差与圆形区域极点的相容性，并对具有指定圆形极点及相容状态方差约束的控制问题给出了满意控制设计方法.用线性矩阵不等式(LMIs)刻划了圆形极点约束下系统存在反馈控制律的充要条件；通过求解LMIs约束下矩阵迹的极值问题，给出了方差约束指标的较好容许范围；算例说明本成果简洁、有效.