Equilibrium Equivalence Theorem and its applications to control and stability analysis

Leon A. Luxemburg, Garng Morton Huang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)111-134
Number of pages24
JournalCircuits Systems and Signal Processing
Volume14
Issue number1
DOIs
Publication statusPublished - 1 Jan 1995
Externally publishedYes

Fingerprint

Equivalence Theorem
Structural Stability
Stability Analysis
Equivalence
Vector Field
Perturbation
Noncompact Manifold
Power System
Dynamical systems
Bifurcation
Dynamical system

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics

Cite this

Equilibrium Equivalence Theorem and its applications to control and stability analysis. / Luxemburg, Leon A.; Huang, Garng Morton.

In: Circuits Systems and Signal Processing, Vol. 14, No. 1, 01.01.1995, p. 111-134.

Research output: Contribution to journalArticle

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