Abstract second order hyperbolic system and applications to controlled network of strings

作者：Xu Gen Qi^*; Liu Dong Yi; Liu Yan Qing

来源：SIAM Journal on Control and Optimization, 2008, 47(4): 1762-1784.

DOI：10.1137/060649367

• hyperbolic system
• spectral distribution
• Riesz basis
• exponential stability
• tree-shaped network

In this paper we study an abstract second order hyperbolic system valued in 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.

• 出版日期2008
• 单位天津大学