Limits of negative definite and nondefinite state weight matrices for second order systems

机译：二阶系统的负定态和非定态权重矩阵的极限

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The relationship between negative definite and nondefinite state weight matrices and closed loop poles in the linear quadratic regulator (LQR) is found for second order systems. The limits of the negative definite and nondefinite state weight matrix are shown to depend on te open loop system eigenvalues. The bounds of the closed loop eigenvalues on the complex plane are related to the geometric mean and the root mean squared of the open loop system eigenvalues. The detailed relationships between the positive definite, nondefinite and negative definite state weight matrices based on various open loop poles are described. Application of the theory is shown through a set of numerical examples. Although the discussion and the examples concern second order systems, the underlying principles are applicable to systems of any order.

机译：对于二阶系统，找到了线性二次调节器（LQR）中的负定状态权矩阵和非定状态权矩阵与闭环极点之间的关系。负定状态权矩阵和非定状态权矩阵的限制显示为取决于开环系统特征值。复平面上闭环特征值的边界与开环系统特征值的几何均值和均方根有关。描述了基于各种开环极点的正定，非定和负定状态权重矩阵之间的详细关系。通过一系列数值示例说明了该理论的应用。尽管讨论和示例涉及二阶系统，但基本原理适用于任何阶数的系统。

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《AIAA guidance, navigation and control conference》|1995年|p.1135-1141|共7页
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Shyh-Pyng Shue; M. E. Sawan; Kamran Rokhsaz;
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中图分类 V3;
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Limits of negative definite and nondefinite state weight matrices for second order systems

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