I have a plant having a pair of real poles
$\lambda_1 = -7.5, \lambda_2 = 7.5$ and I want to derive the minimum closed-loop bandwidth required to properly control the plant.
By looking at the doubling time (Ref. Etkin, Reid, "Dynamics of Flight: Stability and Control", page 164), defined as
$\frac{\log(2)}{\max{Re(\lambda)}}$ I see that for my system the doubling time is 0.09 s.
How do I relate this value to the minimum required closed-loop bandwidth that my controller has to have?
Thanks!