Exponential input-to-state stability of globally Lipschitz time-delay systems under sampled-data noisy output feedback and actuation disturbances

In this paper we deal with the problem of global exponential practical stability preservation for globally Lipschitz time-delay systems, by Euler emulation of continuous-time dynamic output feedback controllers affected by measurement noises and actuation disturbances. Nonlinear time-delay systems not necessarily affine in the control input are studied. It is shown that, if the continuous-time closed-loop system at hand is globally exponentially stable and the maps describing the plant and the continuous-time dynamic output feedback controller are globally Lipschitz, then, under suitably fast sampling, the Euler emulation of the continuous-time controller at hand preserves the global exponential stability of the sampled-data closed-loop system (no matter whether periodic or aperiodic sampling is used). In the case of bounded measurement noises and bounded actuation disturbances affecting the control law, it is proved that, under suitable fast sampling, (global) exponential input-to-state stability with respect to both these external inputs is guaranteed. A generalisation of the Halanay's inequality is used as a tool in order to prove the results. The existence of a Lyapunov-Krasovskii functional for the continuous-time closed-loop system is sufficient to ensure the preservation of the global exponential practical stability. On the other hand, the explicit knowledge of a Lyapunov-Krasovskii functional allows us to compute an upper bound for the sampling period. An example is presented which validates the theoretical results.