On the number of unstable equilibria of a class of nonlinear systems

New Results on the stability region of a class of nonlinear system and the number of equilibrium points on its boundary are presented in this paper. New concepts such as general position of and regularity of stability regions, are developed. Based on these two conditions. together with the general topological arguments, the power bound and upper bound on the number of unstable equilibrium points are obtained. These bounds can be used to estimate the computational load required to construct the stability boundary.