Index Analysis of Differential‐Algebraic Equation Models for Electric Circuits With Gyrators

This paper investigates the index of differential‐algebraic equations (DAEs) that arise in modeling of electric circuits with gyrators. A gyrator is a two‐port network element whose constitutive equations are defined by a skew‐symmetric matrix. While the index analysis of DAEs in circuit simulation has been extensively studied, the existing characterizations are not applicable to circuits that include gyrators. For linear time‐invariant circuits with gyrators, we analyze the index of DAEs using a matroid‐theoretic approach. We show that the problem of determining whether DAEs arising from the hybrid analysis have index at most one or not is reduced to a linear matroid parity problem. We also provide a structural characterization for DAEs arising from the modified nodal analysis (MNA), and extend it to nonlinear circuits, generalizing a structural characterization that is well known in the index analysis of the MNA models.