Exponential stability of abstract evolution equations with time delay (1405.1850v2)

Abstract: We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a suitable smallness condition on the time delay feedback is satisfied. Some examples illustrating our abstract approach are also given.