Riesz Basis and Stability Analysis of the Feedback Controlled Networks of 1-D Wave equations

Hits:

Journal:WSEAS TRANSACTIONS on MATHEMATICS

Key Words:wave equation, partial differential network, geometrically continuous type network, Riesz basis

Abstract:In this paper, using graph theory and functional analysis approach, we study the Riesz basis property and the stabilization of general networks of 1-D wave equations. Firstly, we derive the vector form of the model under
consideration and then discuss the controllers design. We prove that the controlled network is a Riesz system under
certain conditions and hence the spectrum determined growth assumption holds. Further we give some necessary
and sufficient conditions for the asymptotic stability and the non-stability of the controlled network by spectral
conditions. Finally, ...

All the Authors:D. Liu, G. Xu

First Author:Dongyi Liu

Indexed by:Unit Twenty Basic Research

Correspondence Author:Dongyi

Volume:11

Issue:5

Page Number:434-455

Translation or Not:no