Stabilization Domains for Second Order Delay Systems

In this paper, an analytic condition is given for determining delayed positive feedback controller for stabilizing an oscillatory system. The
$\tau $
-decomposition and
$D$
-decomposition methods are employed in deriving this condition. The obtained results are then used to stabilize second order delay systems by a proportional controller. Under-damped and over-damped systems are treated separately, where the Smith-predictor structure is used in the over-damped case to obtain the stability conditions. Illustrative examples are given to show the effectiveness of the proposed approach.