A generalization of monotonicity applied to the DC analysis of nondifferentiable resistive networks

The dc analysis of an important class of nondifferentiable nonlinear resistive networks is considered which include both piecewise linear and continuously differentiable cases. A local -functional is introduced to generalize a concept of monotonicity, and its useful properties are shown. The existence and uniqueness property of dc operating points is investigated in this class of resistive networks in terms of the local -functional. Relations to previous concepts such as positive definiteness and monotone operators are clarified.