Convergence analysis of nonlinear dynamical systems by nested Lyapunov functions

Author

Peterfreund, N. ; Baram, Y.

Author_Institution

Center for Eng. Syst. Adv. Res., Oak Ridge Nat. Lab., TN, USA

Volume

43

Issue

8

fYear

1998

fDate

8/1/1998 12:00:00 AM

Firstpage

1179

Lastpage

1184

Abstract

A method for estimating the domain of attraction of an asymptotically stable equilibrium point of a nonlinear dynamical system and for deriving an upper bound on the time of convergence in the estimated domain is presented. It is based on a set of Lyapunov functions. Defined on nested regions in the state space. The estimated domain, obtained as the union of a subset of these regions, is based on a local Lyapunov-like condition for the convergence of the solution in each region to its inner boundary. A bound on the time of convergence within the estimated domain is given by the sum of the local bounds. This concept is implemented using a class of regions whose boundaries are described by Fourier series

Keywords

Fourier series; Lyapunov methods; convergence; nonlinear dynamical systems; state-space methods; Fourier series; asymptotically stable equilibrium point; convergence analysis; domain of attraction; local Lyapunov-like condition; nested Lyapunov functions; nonlinear dynamical systems; Convergence; Enterprise resource planning; Fourier series; Lyapunov method; NASA; Nonlinear dynamical systems; Power engineering and energy; State-space methods; Systems engineering and theory; Upper bound;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.704997

Filename

704997