Stabilization of wave systems with input delay in the boundary control

By G. Xu, Siu Pang Yung, Leong-Kwan Li. 2006

329 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1db1ccfe5e358f1fc95aeb65567ff9df5db473aa

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Exponential stability of the wave equation with boundary time-varying delay (2010, background): “The above problem, with both µ 1 , µ 2 > 0 and a constant delay τ, has been studied in one space dimension by Xu, Yung and Li [28], on networks by Nicaise and Valein [24] and in higher space dimension by Nicaise and Pignotti [23].”
General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback (2012, background): “For example, it was proved in [9, 10, 21, 22, 30] that an arbitrarily small delay may destabilize a system which is uniformly asymptotically stable in the absence of delay unless additional conditions or control terms have been used.”
Stabilization of the wave equation with boundary or internal distributed delay (2008, background): “If μ0 > μ1 exponential stability is proved from Xu, Yung and Li [24] in the one dimensional case and by the authors in general space dimension [20].”
Feedback stabilization of a class of evolution equations with delay (2009, methodology): “These results have been obtained in the case of one dimensional systems in [ 29 ] by a direct spectral method.”
STABILIZATION OF SECOND ORDER EVOLUTION EQUATIONS WITH UNBOUNDED FEEDBACK WITH DELAY (2010, background): “3) is not satisfied, there exist cases where some instabilities may appear (see [16,17,23] for the wave equation).”
Stability analysis of Euler‐Bernoulli beam with input delay in the boundary control (2012, background): “In [6], the authors considered the feedback control with input delay of this form for a wave system, in which = and =(1− ).”
Exponential stability of abstract evolution equations with time delay (2014, unknown): “[4, 5, 6, 9, 16]) that they can induce some instability.”
INTERIOR FEEDBACK STABILIZATION OF WAVE EQUATIONS WITH TIME DEPENDENT DELAY (2011, methodology): “The analogous problem with boundary feedback has been introduced and studied by Xu, Yung, Li [29] in one-space dimension using a fine spectral analysis and in higher space dimension by the authors [23].”
Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks (2006, methodology): “Here, in agreement with [17] we obtain a stabilization result in a general space dimension by using a suitable observability estimate.”