An example for the switching delay feedback stabilization of an infinite dimensional system: the boundary stabilization of a string

DOI10.1016/j.sysconle.2011.01.004zbMath1216.93084OpenAlexW2043966287WikidataQ104129280 ScholiaQ104129280MaRDI QIDQ533794

Marius Tucsnak, Martin Gugat

Publication date: 6 May 2011

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.sysconle.2011.01.004

zbMATH Keywords

wave equationdelayboundary feedbackstringhyperbolic PDEswitching delayfeedback with delayfeedback stabilization of PDEspast observation

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Wave equation (35L05)

Related Items (15)

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Cites Work

• Unnamed Item
• Feedback stabilization of a class of evolution equations with delay
• Feedback boundary stabilization of wave equations with interior delay
• Stabilization of the wave equation with variable coefficients and a delay in dissipative boundary feedback
• Some second-order vibrating systems cannot tolerate small time delays in their damping
• Dynamic stabilization of an Euler-Bernoulli beam equation with time delay in boundary observation
• Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation
• Boundary feedback stabilization by time delay for one-dimensional wave equations
• Optimal boundary control of a string to rest in finite time with continuous state
• Optimal Energy Control in Finite Time by varying the Length of the String
• Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
• An Example on the Effect of Time Delays in Boundary Feedback Stabilization of Wave Equations
• The rate at which energy decays in a string damped at one end
• Conditions for Robustness and Nonrobustness of the Stability of Feedback Systems with Respect to Small Delays in the Feedback Loop
• Optimal boundary feedback stabilization of a string with moving boundary

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