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.
Descriptors:
Subject Categories:
- Theoretical Mathematics
- Operations Research
- Cybernetics