On global exponential stability preservation under sampling for globally Lipschitz time-delay systems

The paper shows that the global exponential stability property is preserved, under suitably fast sampling and small input-delay, whenever the dynamics of the time-delay system at hand and the related stabilizing (in continuous-time) state feedback are described by globally Lipschitz maps. The Halanay's inequality is used in order to prove this result. Continuous-time, possibly non-affine in the control, state-delay systems are considered. The knowledge of a Lyapunov-Krasovskii functional for the continuous-time closed-loop system is not required, as long as this system is globally exponentially stable. The knowledge of a Lipschitz Lyapunov-Krasovskii functional allows for an estimation of the sampling period that preserves the exponential stability, as well as of the decay rate.