A Sufficient Condition on Riesz Basis with Parentheses of Non-Self-Adjoint Operator and Application to a Serially Connected String System under Joint Feedbacks

Authors:
Bao-Zhu Guo;Yu Xie
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2004

Citing 0
Cited 4

Stability and Riesz basis property for general network of strings

Journal of Dynamical and Control Systems
Brief paper: Arbitrary decay rate for two connected strings with joint anti-damping by boundary output feedback

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Stabilization and Riesz basis of a star-shaped network of Timoshenko beams

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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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Abstract

This paper gives an abstract sufficient condition on Riesz basis with parentheses property for the generators of C0-groups in Hilbert spaces whose eigenvalues are comprised of some finite unification of separable sets after taking the algebraic multiplicities into account. The condition is then applied to the closed-loop system of a serially connected string system under joint damping feedbacks to show that there is a family of generalized eigenfunctions that form a Riesz basis with parentheses in the state space. The spectrum-determined growth condition is concluded as a consequence.