Complete stability of linear time-delay systems: A new frequency-sweeping frequency approach

The complete stability of time-delay systems (TDSs) has not been fully investigated so far, though this issue has attracted considerable attention. In order to systematically solve this problem, we need to study two critical properties: the invariance and the ultimate stability properties. In this paper, we present a new frequency-sweeping approach, by using which we can prove the invariance property and then find the ultimate stability condition for the first time. In addition, we will show that the proposed frequency-sweeping framework is a unified approach. We can obtain the complete stability of a TDS by only performing the frequency-sweeping test.