Fridman, Emilia; Nicaise, Serge; Valein, Julie Stabilization of second order evolution equations with unbounded feedback with time-dependent delay. (English) Zbl 1214.93081 SIAM J. Control Optim. 48, No. 8, 5028-5052 (2010). Summary: We consider abstract second-order evolution equations with unbounded feedback with time-varying delay. Existence results are obtained under some realistic assumptions. We prove the exponential decay under some conditions by introducing an abstract Lyapunov functional. Our abstract framework is applied to the wave, to the beam, and to the plate equations with boundary delays. Cited in 33 Documents MSC: 93D15 Stabilization of systems by feedback 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93C20 Control/observation systems governed by partial differential equations 70Q05 Control of mechanical systems Keywords:second-order evolution equations; wave equations; time-varying delay; stabilization; Lyapunov functional PDFBibTeX XMLCite \textit{E. Fridman} et al., SIAM J. Control Optim. 48, No. 8, 5028--5052 (2010; Zbl 1214.93081) Full Text: DOI