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由于协方差配置理论可以比传统的控制设计方法更直接地将闭环系统的状态协方差配置到指定值，因此该理论成为近年来人们研究的一个热点。然而，在已有的基于输出反馈的离散系统协方差控制文献中均未考虑测量噪声的影响。为此，该文研究含测量噪声的线性离散随机系统的输出反馈协方差控制问题，即设计输出反馈控制器，使闭环系统达到预先给定的稳态状态协方差。基于矩阵分解技巧和广义逆理论，文中导出了期望控制器存在的充要条件及其解析表达式。示例说明了该文设计方法的直接性和有效性。
The theory of covariance configuration can be used to assign the state covariance of the closed-loop system more directly to the specified value than the traditional control design method. Therefore, this theory has become a hot spot in recent years. However, the influence of measurement noise is not considered in the existing discrete system covariance control based on output feedback. For this reason, this paper studies the output feedback covariance control problem of linear discrete stochastic systems with measurement noise, ie, designing the output feedback controller to make the closed-loop system reach the predetermined steady-state covariance. Based on the matrix decomposition technique and the generalized inverse theory, the necessary and sufficient conditions for the existence of a desired controller and its analytical expressions are derived. The example shows the directness and validity of the design method.