Matrix analysis
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
Differential algebraic systems anew
Applied Numerical Mathematics
Non-linear circuit modelling via nodal methods: Research Articles
International Journal of Circuit Theory and Applications
Time-domain properties of reactive dual circuits: Research Articles
International Journal of Circuit Theory and Applications
Tree-based characterization of low index circuit configurations without passivity restrictions
International Journal of Circuit Theory and Applications
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Cyclic matrices of weighted digraphs
Discrete Applied Mathematics
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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.