Semi–Global Exponential Stabilization of Nonlinear Time–Delay Systems via Sampled–Data Event–Triggered Controllers

In this paper, the sampled-data event-triggered stabilization problem of nonlinear time-delay systems is addressed. In particular, a methodology for the design of sampled- data event-triggered exponential stabilizers is provided for locally Lipschitz nonlinear systems not necessarily affine in the control input and in presence of state delays. As a first step, the new notion of Steepest Descent Exponential Feedbacks (SDEFs) is introduced. Then, it is shown that there exists a suitably fast sampling such that the digital implementation of SDEFs, updated through a proposed event-triggered mechanism, ensures the semi-global exponential stability property of the corresponding closed-loop system. The stabilization in the sample-and-hold sense theory and the Halanay's inequality approach are used as tools to prove the results. In the proposed methodology, the inter-sampling system behaviour as well as time-varying sampling intervals are taken into account. Moreover, delay-free systems are included as a special case. The results are validated through a numerical example.