DAEs in Circuit Modelling: A Survey

This paper surveys different analytical aspects of differential-algebraic models of electrical and electronic circuits. The use of DAEs in circuit modelling has increased in the last two decades, and differential-algebraic (or semistate) models play nowadays a key role in circuit simulation programs and also in the analysis of several aspects of nonlinear circuit dynamics. We discuss not only nodal systems, including MNA, but also branch-oriented and hybrid ones, as well as the models arising in other approaches to circuit analysis. Different results characterizing the index of DAE models, for both passive and active circuits, are reviewed in detail. We also present a detailed discussion of memristive devices (memristors, memcapacitors and meminductors), displaying a great potential impact in electronics in the near future, and address how to accommodate them in differential-algebraic models. Some dynamical aspects and other topics in circuit theory in which DAEs play a role, regarding e.g. model reduction, coupled problems or fault diagnosis, are discussed in less detail.

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