Equilibrium Equivalence Theorem and its applications to control and stability analysis Academic Article uri icon


  • This article studies dynamical systems under perturbations. We prove an Equilibrium Equivalence Theorem that guarantees that the dynamics of the system remains unchanged under perturbations with certain fairly general assumptions. We also prove that a power system is robust with respect to parameter changes in generic situations. Concepts of equilibrium equivalence and equilibrium equivalence structural stability are developed and are applied to studies of bifurcations of vector fields on noncompact manifolds. A constructive approach to equilibrium equivalence structural stability verification is emphasized. General results on structural stability of vector fields on differential manifolds are established and important applications of this theory to stability analysis are considered. ¬© 1995 Birkh√§user.

author list (cited authors)

  • Luxemburg, L. A., & Huang, G. M.

citation count

  • 3

publication date

  • January 1995