Stability analysis of damped SDOF systems with two time delays in state feedback

This paper presents the stability analysis of linear, damped SDOF vibration control systems with two time delays, one in the displacement feedback and the other in the velocity feedback. First, a sufficient and necessary algebraic criterion is proved to check the system stability independent of time delays. According to this criterion, all possible combinations of the feedback gains that guarantee the delay-independent stability are given. Then, the effect of the feedback gains on the system stability is discussed when the time delays are finite. The most dangerous case is found when the time delay in the displacement feedback is much longer than that in the velocity feedback.