Stabilization of Lebesgue's sampled systems with bounded controls: the chain of integrators case

International audienceIn this paper, the stabilization of a chain of integrators in the Lebesgue sampling context is considered. Lebesgue sampling refers to a sampling scheme where measurements are not taken at periodic instants but when variables crosse a priori defined levels. The paper proposes a nonlinear control law that stabilizes the system in the sense that it renders asymptotically stable any a priori given hyper-rectangle strictly larger and encompassing the smallest set where the states fail to be detectable because of the quantization precision. The control law is a sum of saturated linear feedback computed with quantized measurements