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Abstract and Applied Analysis
Volume 2014, Article ID 724512, 10 pages
http://dx.doi.org/10.1155/2014/724512
Research Article

A New Approach for the Stability Analysis of Wave Networks

1College of Science, Civil Aviation University of China, Tianjin 300300, China
2Department of Mathematics, Tianjin University, Tianjin 300072, China

Received 12 February 2014; Accepted 19 April 2014; Published 11 May 2014

Academic Editor: Marco Donatelli

Copyright © 2014 Ya Xuan Zhang and Gen Qi Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a new approach to investigate the stability of controlled tree-shaped wave networks and subtrees of complex wave networks. It is motivated by regarding the network as branching out from a single edge. We present the recursive relations of the Laplacian transforms of adjacent edges of the system in its branching order, which form the characteristic equation. In the stability analysis, we estimate the infimums of the recursive expressions in the inverse order based on the spectral analysis. It is a feasible way to check whether the system is exponentially stable under any control strategy or parameter choice. As an application we design the control law and study the stability of a 12-edge tree-shaped wave network.