Stability Analysis and Control Design of a Vibration Control System with Uncertain and Tunable Delays∗

Vibrations being induced on a main structure due to ?uctuating force disturbances are suppressed in this study using Delayed Resonator (DR) (N. Olgac, M. Hosek, 1997), with the added challenges that the corresponding system characteristic equation is of neutral type with two independent delays, where one delay must be tuned as per DR and the other is uncertain due to remote communication delays. In this study, a type of Rekasisus transformation with frequency sweeping approach is adopted along with D-subdivision theorem for the stability analysis of the LTI vibration control problem with respect to uncertain delay and controller gains, while keeping the tuned delay fixed, similar to that in (Cooke and van den Driessche, 1986a). Simulations, which validate the results, are also presented.