Stability and Consensus of Electrical Circuits via Structural Properties

In this paper stability and consensus on electrical circuits is approached. The novelty of the presented results lies in the fact that, contrary to the usual practice of establishing these properties for a given circuit, generic features of this class of networks are interpreted in terms of interconnections of the circuit elements to conceive specific topologies for which both stability and consensus are guaranteed. Fundamental for this achievement is the Hamiltonian structure exhibited by the circuits, since the features enjoyed by this kind of dynamical systems allow to systematically state the structural (interconnection) properties under which stability is assured while conditions to conclude consensus are derived from the analysis of its equilibria.