Predictor-Feedback Stabilization of Globally Lipschitz Nonlinear Systems with State and Input Quantization

Abstract: We develop a switched nonlinear predictor-feedback control law to achieve global asymptotic stabilization for nonlinear systems with arbitrarily long input delay, under state quantization. The proposed design generalizes the nonlinear predictor-feedback framework by incorporating quantized measurements of both the plant and actuator states into the predictor state formulation. Due to the mismatch between the (inapplicable) exact predictor state and the predictor state constructed in the presence of state quantization, a global stabilization result is possible under a global Lipschitzness assumption on the vector field, as well as under the assumption of existence of a globally Lipschitz, nominal feedback law that achieves global exponential stability of the delay and quantization-free system. To address the constraints imposed by quantization, a dynamic switching strategy is constructed, adjusting the quantizer's tunable parameter in a piecewise constant manner-initially increasing the quantization range, to capture potentially large system states and subsequently refining the precision to reduce quantization error. The global asymptotic stability of the closed-loop system is established through solutions estimates derived using backstepping transformations, combined with small-gain and input-to-state stability arguments. We also extend our approach to the case of input quantization.