Disturbance attenuation limitations for systems with input delays

In this work it is shown that for every time-delay system there is a fundamental limitation to the disturbance attenuation that can be achieved by any possible feedback stabilizer. More specifically, there is a lower bound to the asymptotic gain of the disturbance and consequently, there is a lower bound for the gain of the disturbance. Explicit formulas are provided for the computation of the lower bound and specific results are provided for Linear Time-Invariant Systems.