Journal Article

The group and Riesz basis properties of string systems with time delay and exact controllability with boundary control

Xu Gen Qi and Jia Jun Guo

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 23, issue 1, pages 85-96
Published in print March 2006 | ISSN: 0265-0754
Published online March 2006 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dni045
The group and Riesz basis properties of string systems with time delay and exact controllability with boundary control

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The group property of a string system with time delay in boundary and the Riesz basis property of eigenvectors of the system are discussed in the present paper. It is proved that, when the feedback with delay τ > 0, the system also associates a C0 group, and its eigenvectors (generalized eigenvectors) form a Riesz basis in Hilbert space ℋ. This result shows that time delay may destroy the stability of the system, but the group and Riesz basis properties are kept. As a consequence, the exact controllability of the system with boundary control is given.

Keywords: string equation; time delay; C0 group; Riesz basis property; exact controllability

Journal Article.  0 words. 

Subjects: Mathematics

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