Structural characterization of classical and memristive circuits with purely imaginary eigenvalues

摘要: SUMMARY The hyperbolicity problem in circuit theory concerns the existence of purely imaginary eigenvalues linearization time-domain description dynamics. In this paper, we characterize configurations that, a strictly passive setting, yield for all values capacitances and inductances. Our framework is based on branch-oriented, semistate (differential-algebraic) models that capture explicitly topology, use several notions results from digraph theory. So-called P-structures arising analysis turn out to be key element supporting our results. The shown hold not only classical (RLC) circuits but also nonlinear including memristors other mem-devices. Copyright © 2011 John Wiley & Sons, Ltd.