Stability of a star-shaped coupled network of strings and beams
MMACTEE'08 Proceedings of the 10th WSEAS International Conference on Mathematical Methods and Computational Techniques in Electrical Engineering
Stability and Riesz basis property for general network of strings
Journal of Dynamical and Control Systems
Stability of a complex network of Euler-Bernoulli beams
WSEAS TRANSACTIONS on SYSTEMS
Spectrum of a complex network of Euler-Bernoulli beams
AMATH'09 Proceedings of the 15th american conference on Applied mathematics
Spectral distribution of a star-shaped coupled network
ICS'08 Proceedings of the 12th WSEAS international conference on Systems
Exponential and Super Stability of a Wave Network
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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In this paper we study an abstract second order hyperbolic system valued in $\mathbb{C}^N$ with appropriate boundary conditions. We prove that the system is well-posed and associates with a $C_0$ semigroup in a Hilbert state space. Under certain conditions, we show that the spectra of the system operator are located in the vertical strip, and that there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis with parentheses for the Hilbert state space, and hence that the system satisfies the spectrum determined growth assumption. As applications, we investigate the exponential stability of a controlled tree-shaped network of 7-strings and a network of $N$-connected strings.