On the Global Convergence of a Class of Homotopy Methods for Nonlinear Circuits and Systems

Homotopy methods are developed for robustly computing solutions of nonlinear equations, which is of fundamental importance in nonlinear circuit and system simulations. This brief develops theoretical results on the global convergence of a class of homotopy methods for solving nonlinear circuits and systems. A set of sufficient conditions that guarantee the global convergence of homotopy methods is derived. These analytical results are then illustrated on a small nonlinear circuit and a large (about 10 000-dimension) power grid.