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Predictor-feedback stabilization of globally Lipschitz nonlinear systems with state/input quantization

Koudohode Florent, Bekiaris-Liberis Nikolaos

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Summary

We develop a switched nonlinear predictor-feedback control law to achieve globalasymptotic stabilization for nonlinear systems with arbitrarily long input delay, under statequantization. The proposed design generalizes the nonlinear predictor-feedback framework byincorporating quantized measurements of both the plant and actuator states into the predictorstate formulation. Due to the mismatch between the (inapplicable) exact predictor state andthe predictor state constructed in the presence of state quantization, a global stabilizationresult is possible under a global Lipschitzness assumption on the vector field, as well asunder the assumption of existence of a globally Lipschitz, nominal feedback law that achievesglobal exponential stability of the delay/quantization-free system. To address the constraintsimposed by quantization, a dynamic switching strategy is constructed, adjusting the quantizer’stunable parameter in a piecewise constant manner—initially increasing the quantization range,to capture potentially large system states and subsequently refining the precision to reducequantization error. The global asymptotic stability of the closed-loop system is establishedthrough solutions estimates derived using backstepping transformations, combined with smallgain and input-to-state stability arguments. We also extend our approach to the case of input quantization.

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