Input-to-state stabilization of linear systems under data-rate constraints

Abstract

We study feedback stabilization of linear systems under data-rate constraints in the presence of completely unknown disturbances. A communication and control strategy is proposed based on sampled and quantized state measurements, where the quantization range is dynamically adjusted using reachable-set approximations and disturbance estimates derived from quantization parameters. The strategy alternates between stabilizing and searching stages to recapture the state after escapes from the quantization range. Under a data-rate condition, it guarantees input-to-state stability (ISS) with respect to the disturbance. An additional quantization symbol is introduced to establish ISS near the equilibrium. A simulation example illustrates the effectiveness of the proposed approach.