Constructive homotopy methods for finding all or multiple DC operating points of nonlinear circuits and systems.

A comprehensive analysis of homotopy methods on the computation of all DC operating points of nonlinear circuits and systems is conducted. Several sufficient conditions for the connectivity of all the solutions along a single homotopy path are derived. These conditions offer criteria to determine a starting point from which one can find all the solutions along one homotopy path. For the class of nonlinear circuits and systems in which all the solutions lie on several homotopy paths, a new systematic method to explicitly construct a starting point for each homotopy paths is developed. From a practical viewpoint, the constructive method developed does not require the difficult task of finding a good initial guess and is applicable to general nonlinear circuits and systems. From a methodological viewpoint, the constructive method developed is applicable to general homotopy methods with different homotopy functions.