Open Access
2014 A New Approach for the Stability Analysis of Wave Networks
Ya Xuan Zhang, Gen Qi Xu
Abstr. Appl. Anal. 2014: 1-10 (2014). DOI: 10.1155/2014/724512


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.


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Ya Xuan Zhang. Gen Qi Xu. "A New Approach for the Stability Analysis of Wave Networks." Abstr. Appl. Anal. 2014 1 - 10, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022953
MathSciNet: MR3212445
Digital Object Identifier: 10.1155/2014/724512

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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