论文标题
在平衡的截断误差上绑定和符号参数从箭头实现
On the balanced truncation error bound and sign parameters from arrowhead realizations
论文作者
论文摘要
线性动力学系统的平衡截断和奇异扰动近似产生降低的模型，该模型满足涉及Hankel单数值的众所周知的误差。我们表明，如果与截短的hankel单数值相对应的符号参数，则该界限具有单输入，单输出系统的平等。这些符号由相应线性模型的广义状态空间对称属性确定。对于具有箭头实现的一类特殊类别的系统，可以直接从相应的箭头矩阵的非对角线条目中确定符号。我们描述了这种箭头系统如何在网络建模的某些应用中自然出现，并通过激发本研究的电力系统模型来说明这些结果。
Balanced truncation and singular perturbation approximation for linear dynamical systems yield reduced-order models that satisfy a well-known error bound involving the Hankel singular values. We show that this bound holds with equality for single-input, single-output systems, if the sign parameters corresponding to the truncated Hankel singular values are all equal. These signs are determined by a generalized state-space symmetry property of the corresponding linear model. For a special class of systems having arrowhead realizations, the signs can be determined directly from the off-diagonal entries of the corresponding arrowhead matrix. We describe how such arrowhead systems arise naturally in certain applications of network modeling, and illustrate these results with a power system model that motivated this study.
