Adaptive stabilization of uncertain nonlinear time-delay systems with quantized input and output

This paper investigates the problem of global output feedback stabilization for a class of uncertain nonlinear time-delay systems with unknown time delay in the states and the input in which both the input and the output are logarithmically quantized. The nonlinear functions of such systems are not completely known and satisfying certain bounded condition depending on the unmeasured states and the input. We construct a new dynamic high-gain observer where only an output quantization instead of the output is available for measurement to dominate the unknown nonlinear functions view as external disturbances. A scaled change of coordinates and an appropriate Lyapunov-Krasovskii functional are derived to achieve the global stabilization in the sense that all the states of such systems are defined, bounded in the maximal interval [0, +infinity), and converge to the zero equilibrium. A numerical example is provided to illustrate the result.