Riesz basis and stabilization for the flexible structure of a symmetric tree‐shaped beam network

DOI10.1002/mma.909zbMath1282.93211OpenAlexW1968947949MaRDI QIDQ5448590

Bao-Zhu Guo, Jun-Min Wang

Publication date: 7 March 2008

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.909

zbMATH Keywords

exponential stabilityspectral analysiscollocated controlbeam network

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Control of mechanical systems (70Q05) Operator-theoretic methods (93B28) General theory of ordinary differential operators (47E05) Schrödinger operator, Schrödinger equation (35J10) Control/observation systems in abstract spaces (93C25)

Related Items (15)

Stabilization of the Timoshenko beam system with restricted boundary feedback controls ⋮ A pinned network of Euler-Bernoulli beams under feedback controls ⋮ Controllability of a multichannel system ⋮ Stabilization and Riesz basis of a star-shaped network of Timoshenko beams ⋮ Exponential stability of Rayleigh beam equation on a star‐shaped network with indefinite damping ⋮ Exponential stabilization of variable coefficient wave equations in a generic tree with small time-delays in the nodal feedbacks ⋮ Asymptotic stability and Riesz basis property for tree-shaped network of strings ⋮ Stabilization of serially connected hybrid PDE–ODE system with unknown external disturbances ⋮ Exponential stabilisation of Euler–Bernoulli beam with uncertain disturbance ⋮ Output feedback stabilisation of a tree-shaped network of vibrating strings with non-collocated observation ⋮ Riesz basis property and stability of planar networks of controlled strings ⋮ Exponential stabilisation of a simple tree-shaped network of Timoshenko beams system ⋮ EXPONENTIAL STABILISATION OF A TREE-SHAPED NETWORK OF STRINGS WITH VARIABLE COEFFICIENTS ⋮ Stability and spectral properties of general tree-shaped wave networks with variable coefficients ⋮ Exponential stability of a network of beams

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• On the analysis and control of hyperbolic systems associated with vibrating networks
• Boundary eigenvalue problems for differential equations \(N\eta=\lambda P\eta\) with \(\lambda\)-polynomial boundary conditions
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• Unnamed Item

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