Abstract: The issue of designing reduced-order LQG controller is considered from the view of information theory.By exploring the description of the internal state information of the system，two approaches based on cross-Gramian matrix by the principle of minimum information loss are proposed to design LQG reduced-order controller.The performances of the reduced-order LQG closed-loop systems are compared with both the high-order LQG closed-loop and the low-order closed-loop system obtained by the minimum K-L information distance controller reduction method.As the numerical simulation shows the reduced-order closed-loop systems obtained by these two approaches have satisfied performances which prove the efficiency of the controller reduction methods.

Key words: controller reduction, information theory, cross-Gramian, minimum information loss, Loop Quantum Gravity（LQG） optimal control

摘要： 从信息论的角度出发，研究了LQG控制器降阶问题。在考察系统内部状态信息描述的基础上，提出了两种基于交叉格莱姆矩阵最小信息损失的LQG控制器降阶方法。将由这两种方法得出的降阶LQG控制器分别与全阶LQG控制器、基于最小K-L信息距离的降阶控制器进行仿真对比研究，比较各闭环系统的控制性能。仿真结果表明，提出的降阶控制器能较好地逼近全阶控制器实现闭环系统性能。

关键词: 控制器降阶, 信息论, 交叉格莱姆矩阵, 最小信息损失, 圈量子引力（LQG）最优控制