Accession Number : AD0681484

Title :   IDENTIFYING PERTURBATIONS WHICH PRESERVE ASYMPTOTIC STABILITY.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Yorke,James A. ; Strauss,Aaron

Report Date : SEP 1968

Pagination or Media Count : 13

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)

Descriptors :   (*DIFFERENTIAL EQUATIONS, PERTURBATION THEORY), (*PERTURBATION THEORY, STABILITY), INEQUALITIES, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE