Explicit formulation of the state equations for a class of degenerate linear networks

The paper deals with the problem of setting up of the equations in explicit normal form for a class of active and/or nonreciprocal linear time-varying networks. The active components are represented by positive and negative resistors and gyrators. Besides conventional degeneracies, the class includes additional degeneracies caused by gyrator interaction. It is shown that a state-variable description exists provided that the gyrators meet some topological conditions. Conditions are stated which guarantee the existence of the state equations of maximal order of complexity and of their unique solution.