Accession Number:

ADA454895

Title:

Families of Liapunov Functions for Nonlinear Systems in Critical Cases

Descriptive Note:

Technical research rept.

Corporate Author:

MARYLAND UNIV COLLEGE PARK SYSTEMS RESEARCH CENTER

Personal Author(s):

Report Date:

1991-10-01

Pagination or Media Count:

36.0

Abstract:

Liapunov functions are constructed for nonlinear systems of ordinary differential equations whose linearized system at an equilibrium point possesses either a simple zero eigenvalue or a complex conjugate pair of simple, pure imaginary eigenvalues. The construction is explicit, and yields parametrized families of Liapunov functions for such systems. In the case of a zero eigenvalue, the Liapunov functions contain quadratic and cubic terms in the state. Quartic terms appear as well for the case of a pair of pure imaginary eigenvalues. Predictions of local asymptotic stability using these Liapunov functions are shown to coincide with those of pertinent bifurcation-theoretic calculations. The development of the paper is carried out using elementary properties of multilinear functions. The Liapunov function families thus obtained are amenable to symbolic computer coding.

Subject Categories:

  • Theoretical Mathematics
  • Operations Research
  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE