Some remarks on the delay stabilizing effect in SISO systems

This note addresses the stabilization problem of a class of SISO systems with a time delay in the input, and explore the stabilizing effect of time delay. More precisely, for a fixed feedback gain such that the closed loop system is unstable when the delay is set to zero, we present necessary and sufficient conditions for the delays such that the stability in closed-loop is achieved, and provide an explicit construction of the controllers. Next, we analyze conditions for preserving the closed-loop stability if parametric or time-varying delay uncertainties are present in the control law. Illustrative examples are also proposed.