A study on asymptotically stable DC operating points of nonlinear resistive circuits

摘要

Practically speaking, it is well known that in a nonlinear resistive circuit with multiple operating points some of them are unstable. However, the problem of specifying the stability of each operating point is still not completely solved. The stability of operating points is often defined in terms of the stability of equilibrium points. Tadeusiewicz derived a sufficient condition for asymptotically stable operating points of nonlinear resistive circuits with dependent current sources on the basis of parallel capacitors. In this paper, we discuss asymptotically stable operating point of nonlinear resistive circuits with dependent current and voltage sources. Our definition about stability of operating points treats a broader class of dynamic circuit than one of Tadeusiewicz. A sufficient condition for identifying asymptotically stable operating points is derived.