Tests of Exponential Stabilization Through Floquet Theory and Act-And-Wait Control

In this paper, we propose tests of exponential stability based on a version of the Floquet theory for delay differential equations of the first order. Our approach allows researchers to preserve the order of equation and to use the classical methods of the Floquet theory for ordinary differential equations. On this basis, new original unexpected results on the exponential stability are proposed. We demonstrate that choosing period of coefficients and delays of the gain in corresponding intervals allows to achieve the exponential stabilization in the cases considered as impossible when the standard technique was applied.