On the invariance principle: generalizations and applications to synchronization

Author

Rodrigues, Hildebrando M. ; Alberto, Luís F C ; Bretas, Newton G.

Author_Institution

Inst. de Ciencias Matematicas, Sao Paulo Univ., Sao Carlos, Brazil

Volume

47

Issue

5

fYear

2000

fDate

5/1/2000 12:00:00 AM

Firstpage

730

Lastpage

739

Abstract

In many engineering and physics problems it is very hard to find a Lyapunov function satisfying the classical version of the LaSalle´s invariance principle. In this work, an extension of the invariance principle, which includes cases where the derivative of the Lyapunov function along the solutions is positive on a bounded set, is given. As a consequence, a larger class of problems may now be considered. The results are used to obtain estimates of attractors which are independent of coupling parameters. They are also applied to study the synchronization of coupled systems, such as coupled power systems and coupled Lorenz systems. Estimates on the coupling term are obtained in order to accomplish the synchronization

Keywords

Lyapunov methods; differential equations; invariance; nonlinear systems; power systems; stability; synchronisation; Lyapunov function; attractors; bounded set; coupled Lorenz systems; coupled power systems; coupled systems; coupling term estimates; invariance principle; synchronization; Biology; Chaos; Chaotic communication; Differential equations; Helium; Mechanical engineering; Physics; Power system stability; Robustness; Systems engineering and theory;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.847878

Filename

847878