On feedback stabilization of nonlinear systems under quantization

The aim of this note is to show how the results in D. Liberzon, "Hybrid feedback stabilization of systems with quantized signals", Automatica, 39, 1543-1554, 2003, concerning asymptotic stabilization using quantized feedback, still hold under the assumption of asymptotic stabilizability only. As a consequence, we are able to examine as special interesting cases nonlinear systems which are e.g. globally asymptotically and locally exponentially stabilizable and stabilizable by dynamic observer-based feedback. The results are also discussed for discrete-time nonlinear systems.