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Mathematical Problems in Engineering
Volume 2016, Article ID 7870462, 13 pages
http://dx.doi.org/10.1155/2016/7870462
Research Article

Dynamic Characterization of Typical Electrical Circuits via Structural Properties

Facultad de Ingeniería, UNAM, Edificio de Posgrado, Segundo Piso, Ciudad Universitaria, 04510 Ciudad de México, Mexico

Received 6 March 2016; Revised 22 July 2016; Accepted 31 July 2016

Academic Editor: Carlo Cosentino

Copyright © 2016 Sofía Avila-Becerril et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The characterization of a class of electrical circuits is carried out in terms of both stability properties and steady-state behavior. The main contribution is the interpretation of the electrical topology (how the elements that conform the circuits are interconnected) in terms of mathematical properties derived from the structure of their models. In this sense, at what extent the topology by itself defines the dynamic behavior of the systems is explained. The study is based on the graph theory allowing capturing, departing from the well-known Kirchhoff laws, the topology of the circuits into several matrices with specific structure. The algebraic analysis of these matrices permits identifying conditions that determine whether the system is stable in the sense of Lyapunov and the kind of steady-state behavior that it exhibits. The approach is mainly focused on typical topologies widely used in practice, namely, radial, ring, and mesh networks.