WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Riesz Basis and Stability Analysis of the Feedback Controlled Networks of 1-D Wave Equations
Authors: ,
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, we apply the obtained results to two networks of special shapes, and analyze their stability by the “irrational dependence”.
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Keywords: Wave equation, partial differential network, geometrically continuous type network, Riesz basis, stability