IDENTIFYING PERTURBATIONS WHICH PRESERVE ASYMPTOTIC STABILITY.

Abstract

Let the zero solution be uniform-asymptotically stable for x' = f(t,x). Estimates are established in terms of the rate of approach to zero of the solutions of x' = f(t,x), on the magnitude of g(t,x) in order that the zero solution be uniform-asymptotically stable for x' = f(t,x) + g(t,x). A new proof and slight extension of Hahn's theorem is given, using these estimates. If f is homogeneous of degree k, then uniform-asymptotic stability is preserved by g(t,x) = o(/x/superscript k). (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1968
Accession Number
AD0681484

Entities

People

  • Aaron Strauss
  • James A. Yorke

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Perturbations

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Nanofabrication and Microfabrication.