Global asymptotic stability of nonlinear circuits related to maximum flow problems

Abstract

Global asymptotic stability of the nonlinear circuit similar to the one proposed by Sato et al. for solving the maximum flow problem is studied in this paper. The circuit consists of two independent DC voltage sources, capacitors and nonlinear resistors. It is proved rigorously that the circuit has a unique equilibrium point which is globally asymptotically stable. From the viewpoint of dynamical systems, the circuit is a cooperative system, and thus some fundamental results concerning the convergence property of cooperative systems play important roles.