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Stabilization of second order evolution equations with unbounded feedback with time-dependent delay. (English) Zbl 1214.93081

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.

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
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