On Stabilization of Nonlinear Time–Delay Systems via Quantized Sampled–Data Dynamic Output Feedback Controllers

Abstract

In this paper we deal with the stabilization problem of nonlinear systems affected by state delays and known time–varying disturbances via quantized sampled–data dynamic output feedback (QSDOF) controllers. In particular, a QSDOF controller for nonlinear time–delay systems is proposed by means of the novel notion of Dynamic Output Steepest Descent Feedback (DOSDF) induced by a general class of Lyapunov-Krasovskii functionals. Then, the theory of the stabilization in the sample–and–hold sense is used in order to show that: there exist a suitably small inter–sampling time and a suitably accurate quantization of the input/output channels such that the semi–global practical stability of the related quantized sampled–data closed–loop system is ensured with arbitrarily small final target ball of the origin. In the theory here developed, time-varying sampling intervals as well as non–uniform quantization of the input/output channels are taken into account. Furthermore, the stable inter–sampling system behaviour is proved. The case of nonlinear delay-free systems is addressed as a special case. An example is presented which validates the theoretical results.