Existence and computation of dc solution of nonlinear networks in a bounded set

It is important to know whether an operating point of a nonlinear network exists in a certain range. We consider dc equations of nonlinear networks which are characterized by continuous functions. Conditions are presented such that a bounded set containing an operating point is determined. The conditions show that close relations exist between eventual passivity and the existence of an operating point in a bounded set. Network examples are included to illustrate the application of the conditions. Piecewise-linear analysis is used to search an operating point in the determined set. If the bounded set is divided into "nonoverlapping" simplices, a continuous piecewise-linear function can be interpolated on it to approximate the function describing the nonlinear network. It turns out that this method preserves properties needed for the implementation of piecewise-linear analysis.