Application of Center Manifold Reduction to System Stabilization

Abstract

The Center Manifold Theorem is applied to the local feedback stabilization of nonlinear systems in critical cases. The paper addresses two particular critical cases for which the system linearization at the equilibrium point of interest is assumed to possess either a simple zero eigenvalue or a complex conjugate pair of simple, pure imaginary eigenvalues. In either case, the noncritical eigenvalues are taken to be stable. The results on stabilizability and stabilization are given explicitly in terms of the nonlinear model of interest in its original form (i.e., before reduction to the center manifold). Moreover, the formulation given in this paper uncovers connections between results obtained using the center manifold reduction and those of an alternative approach.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1991
Accession Number
ADA454808

Entities

People

  • Der-cherng Liaw
  • Eyad H. Abed

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Eigenvalues
  • Electrical Engineering
  • Engineering
  • Information Operations
  • Maryland
  • Nonlinear Dynamics
  • Nonlinear Systems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Linear Algebra