New equilibrium equivalence concept and its applications to robustness analysis of nonlinear systems

Leon A. Luxemburg, Garng Morton Huang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper proposes and investigates a new equilibrium equivalence concept, which is more general than the conventional topological equivalence concept but offers easier analysis and better engineering insights for nonlinear system design. We prove an equilibrium Equivalence Theorem which guarantees the robustness of the system dynamics under structured perturbations with certain fairly general assumptions. Concepts of Equilibrium Equivalence and Equilibrium Equivalence Structural Stability are developed and applied to studies of bifurcations of vector fields on noncompact manifolds. Constructive approach to Equilibrium Equivalence Structural Stability verification is emphasized. Some applications to nonlinear stability analysis are demonstrated.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherPubl by IEEE
Pages1494-1500
Number of pages7
Volume2
ISBN (Print)0780312988
Publication statusPublished - 1 Dec 1993
Externally publishedYes
EventProceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4) - San Antonio, TX, USA
Duration: 15 Dec 199317 Dec 1993

Other

OtherProceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4)
CitySan Antonio, TX, USA
Period15/12/9317/12/93

Fingerprint

Robustness Analysis
Nonlinear systems
Nonlinear Systems
Equivalence
Structural Stability
Structured Perturbations
Topological Equivalence
Dynamical systems
Equivalence Theorem
Systems analysis
Noncompact Manifold
Nonlinear Stability
Nonlinear Analysis
System Dynamics
System Design
Stability Analysis
Vector Field
Bifurcation
Concepts
Robustness

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Luxemburg, L. A., & Huang, G. M. (1993). New equilibrium equivalence concept and its applications to robustness analysis of nonlinear systems. In Proceedings of the IEEE Conference on Decision and Control (Vol. 2, pp. 1494-1500). Publ by IEEE.

New equilibrium equivalence concept and its applications to robustness analysis of nonlinear systems. / Luxemburg, Leon A.; Huang, Garng Morton.

Proceedings of the IEEE Conference on Decision and Control. Vol. 2 Publ by IEEE, 1993. p. 1494-1500.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Luxemburg, LA & Huang, GM 1993, New equilibrium equivalence concept and its applications to robustness analysis of nonlinear systems. in Proceedings of the IEEE Conference on Decision and Control. vol. 2, Publ by IEEE, pp. 1494-1500, Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4), San Antonio, TX, USA, 15/12/93.
Luxemburg LA, Huang GM. New equilibrium equivalence concept and its applications to robustness analysis of nonlinear systems. In Proceedings of the IEEE Conference on Decision and Control. Vol. 2. Publ by IEEE. 1993. p. 1494-1500
Luxemburg, Leon A. ; Huang, Garng Morton. / New equilibrium equivalence concept and its applications to robustness analysis of nonlinear systems. Proceedings of the IEEE Conference on Decision and Control. Vol. 2 Publ by IEEE, 1993. pp. 1494-1500
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