کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
421302 | 684186 | 2010 | 18 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Augmented nodal matrices and normal trees Augmented nodal matrices and normal trees](/preview/png/421302.png)
Augmented nodal matrices play an important role in the analysis of different features of electrical circuit models. Their study can be addressed in an abstract setting involving two- and three-colour weighted digraphs. By means of a detailed characterization of the structure of proper and normal trees, we provide a unifying framework for the rank analysis of augmented matrices. This covers in particular Maxwell’s tree-based determinantal expansions of (non-augmented) nodal matrices, which can be considered as a one-colour version of our results. Via different colour assignments to circuit devices, we tackle the DC-solvability problem and the index characterization of certain differential–algebraic models which arise in the nodal analysis of electrical circuits, extending several known results of passive circuits to the non-passive context.
Journal: Discrete Applied Mathematics - Volume 158, Issue 1, 6 January 2010, Pages 44–61