Robust Quantized Sampled–Data Stabilization for a Class of Lipschitz Nonlinear Systems With Time–Varying Uncertainties

In this letter, a robust quantized sampled-data controller is provided for a class of nonlinear systems affected by time-varying uncertainties, actuation disturbances and measurement noises. Sufficient conditions based on linear matrix inequalities and ensuring the existence of the proposed robust quantized sampled-data controller are given. Quantization of both state measurements and input signals is simultaneously considered. Input-to-state stability redesign technique is used in order to attenuate the effects of bounded actuation disturbances and of bounded observation errors. It is proved that, under suitably fast sampling and accurate quantization of the input/output channels, the proposed controller achieves the semi-global practical stability, with arbitrarily small final target ball, of the related quantized sampled-data closed-loop system provided that the observation errors do not affect (or affect marginally) the robustification term added in the controller and, that the bounds of the actuation disturbances as well as of the observation errors are a priori known. The theory here developed includes also the cases of time-varying sampling intervals and of non-uniform quantization of the input/output channels as well as the stability analysis of the inter-sampling system behavior. The provided results are validated through an example of one-link manipulator.