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考虑了线性离散随机系统在估计误差方差和H_∞范数约束下的状态估计问题，即设计滤波增益，使系统每个状态分量的估计误差方差的稳态值不大于预先指定值，同时从扰动到误差状态输出的传递函数也满足预先给定的H_∞范数约束。给出了期望滤波增益的存在条件及其解析表达式，并用数值算例说明了本文设计方法的直接性和有效性。
The state estimation of linear discrete-time random systems under the constraints of estimation error variance and H_∞norm is considered. The filter gain is designed so that the steady-state value of the estimated error variance of each state component of the system is not greater than the pre-specified value. The transfer function to the error state output also satisfies the pre-specified H_∞ norm constraint. The existence conditions of the expected filtering gain and its analytical expressions are given. Numerical examples are given to illustrate the directness and validity of the design method.