Linear matrix inequality tests for synchrony of diffusively coupled nonlinear systems

Author

Arcak, Murat

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA

fYear

2010

fDate

Sept. 29 2010-Oct. 1 2010

Firstpage

1651

Lastpage

1656

Abstract

In a recent publication we presented a condition that guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction-diffusion PDE with Neumann boundary conditions. This condition makes use of the Jacobian matrix of the reaction terms and the second Neumann eigenvalue of the Laplacian operator on the given spatial domain. In the present paper we derive an analogous result for the synchronization of a network of identical ODE models coupled by diffusion terms.

Keywords

Jacobian matrices; Laplace equations; eigenvalues and eigenfunctions; linear matrix inequalities; network theory (graphs); nonlinear systems; reaction-diffusion systems; synchronisation; Jacobian matrix; Laplacian operator; Neumann boundary conditions; Neumann eigenvalue; ODE models; diffusively coupled nonlinear system synchronisation; linear matrix inequality tests; reaction-diffusion PDE; Boundary conditions; Eigenvalues and eigenfunctions; Equations; Jacobian matrices; Laplace equations; Linear matrix inequalities; Synchronization;

fLanguage

English

Publisher

ieee

Conference_Titel

Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on

Conference_Location

Allerton, IL

Print_ISBN

978-1-4244-8215-3

Type

conf

DOI

10.1109/ALLERTON.2010.5707114

Filename

5707114