Modeling and Stability Analysis of a Wave Network with Parallel Edges and Loops

2010 ◽  
Author(s):  
Yaxuan Zhang ◽  
Genqi Xu
Keyword(s):  
Stability Analysis ◽  
Wave Network

scholarly journals A New Approach for the Stability Analysis of Wave Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ya Xuan Zhang ◽  
Gen Qi Xu
Keyword(s):  
Stability Analysis ◽  
Control Law ◽  
Single Edge ◽  
Parameter Choice ◽  
New Approach ◽  
Complex Wave ◽  
Exponentially Stable ◽  
The Stability ◽  
Wave Network ◽  
Recursive Relations

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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