On Practical Stability Preservation under Fast Sampling and Accurate Quantization of Feedbacks for Nonlinear Time-Delay Systems

In this article, we deal with the problem of stabilizing a nonlinear system with state-delays by means of quantized sampled-data state feedback control laws. Quantization in the state measurements and in the input signal are simultaneously considered. Fully nonlinear (i.e., possibly nonaffine in the control) time-delay systems are studied. Sufficient conditions are provided such that suitably fast sampling and accurate quantization of the state feedback at hand yield semiglobal practical stability, with arbitrarily small final target ball of the origin. Nonlinear delay-free systems are addressed as a special case: it is shown that the above sufficient conditions, ensuring the semiglobal practical stability, are satisfied if the continuous-time static state feedback controller is a global stabilizer. The theory of stabilization in the sample-and-hold sense is used. The theoretical results are validated through an example.