DAE‐Based Modeling of Electrical Circuits: Classical Methods Revisited and Recent Results

We survey in this communication several topics involving the use of differential‐algebraic equations (DAEs) in nonlinear circuit modeling. Two model families are considered, supported on a nodal‐ and a branch‐oriented approach, respectively. Concerning nodal methods, of primary importance in the numerical simulation of circuit dynamics, we review index characterizations in both passive and active contexts. Branch‐oriented models make it possible to frame in a DAE context Bashkow’s and Bryant’s classical methods for the state formulation problem, as well as to accommodate recent techniques used to set up circuit equations and to tackle certain qualitative properties of circuit dynamics. The emphasis is on the mathematical framework supporting the results, mainly based on applied linear algebra and digraph theory.