Accession Number:

ADA454841

Title:

Families of Liapunov Functions for Nonlinear Systems in Critical Cases

Descriptive Note:

Research rept.

Corporate Author:

MARYLAND UNIV COLLEGE PARK SYSTEMS RESEARCH CENTER

Personal Author(s):

Report Date:

1990-02-01

Pagination or Media Count:

33.0

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 this paper is carried out using elementary properties of multilinear functions. The Liapunov function families thus obtained are amenable to symbolic computer coding.

Subject Categories:

  • Statistics and Probability
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE