Model Reduction by Balanced Truncation of Linear Systems with a Quadratic Output
Model Reduction by Balanced Truncation of Linear Systems with a Quadratic Output
复制标题
通过具有二次输出的线性系统的平衡截断来简化模型
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
K. Meerbergen
中科院分区：
文献类型：
--
作者：
R. Beeumen;K. Meerbergen
平衡截断是线性系统中广泛使用和受欢迎的基于投影的模型降阶技术。这种技术有以下两个重要的性质：平衡截断近似保持稳定性，误差系统的H∞范数（频率响应的最大值）有界于被忽略奇异值之和的两倍以上。本文试图将线性平衡截断的框架扩展到具有二次输出的系统。对于这样的系统，可控性Gramian保持不变。可观测性Gramian是从具有多个输出的线性系统计算的，该输出是从原始系统的二次输出导出的。我们给出了一个由结构分析产生的大规模系统的数值例子。
Balanced truncation is a widely used and appreciated projection‐based model reduction technique for linear systems. This technique has the following two important properties: approximations by balanced truncation preserve the stability and the H∞‐norm (the maximum of the frequency response) of the error system is bounded above by twice the sum of the neglected singular values. This paper tries to extend the framework of linear balanced truncation to systems with a quadratic output. For such systems, the controllability Gramian remains the same. The observability Gramian is computed from a linear system with multiple outputs that is derived from the quadratic output of the original system. We give a numerical example for a large‐scale system arising from structural analysis.