  This paper introduces an innovative method for ensuring global stability in a
broad array of nonlinear systems. The novel approach enhances the traditional
analysis based on Jacobian matrices by incorporating the Taylor series boundary
error of estimation and the eigenvalues of the Hessian matrix, resulting in a
fresh criterion for global stability. The main strength of this methodology
lies in its unrestricted nature regarding the number of equilibrium points or
the system's dimension, giving it a competitive edge over alternative methods
for global stability analysis. The efficacy of this method has been validated
through its application to two established benchmark systems within the
industrial domain. The results suggest that the expanded Jacobian stability
analysis can ensure global stability under specific circumstances, which are
thoroughly elaborated upon in the manuscript. The proposed approach serves as a
robust tool for assessing the global stability of nonlinear systems and holds
promise for advancing the realms of nonlinear control and optimization.
