Nonlinear Monotone Networks
C. Desoer, Felix F. Wu · SIAM Journal on Applied Mathematics · 1974
This paper presents some fundamental results on nonlinear networks with uncoupled, monotone increasing, but not necessarily surjective characteristics. Necessary and sufficient conditions are obtained for the existence and uniqueness of solutions for strictly increasing resistive networks and a general class of increasing resistive networks. They are also necessary and sufficient for the existence of solutions for increasing resistive networks. These conditions are sufficient for the existence of solutions for eventually strictly increasing resistive networks, and for a class of eventually increasing resistive networks. The conditions are circuit-theoretic and can readily be used as a criterion in design. The dependence of solutions on the inputs is studied and also a bounded-input bounded-solution result is presented. Existence and uniqueness results for monotone RLC networks are obtained by viewing them as combinations of three one-element-kind subnetworks. Finally, two algorithms are given for testing the conditions.