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

TL;DR

This paper presents a novel feedback stabilization method for continuous-time linear systems with finite data-rate constraints, using dynamic quantization and disturbance estimation to ensure input-to-state stability.

Contribution

It introduces a new control strategy that guarantees ISS under data-rate constraints, improving upon prior practical stability results.

Findings

Guarantees input-to-state stability with finite data-rate.

Employs dynamic quantization range adjustment based on reachable sets.

Simulation confirms effectiveness of the proposed approach.

Abstract

We study feedback stabilization of continuous-time linear systems under finite data-rate constraints in the presence of unknown disturbances. A communication and control strategy based on sampled and quantized state measurements is proposed, where the quantization range is dynamically adjusted using reachable-set propagation and disturbance estimates derived from quantization parameters. The strategy alternates between stabilizing and searching stages to handle escapes from the quantization range and employs an additional quantization symbol to ensure robustness near the equilibrium. It guarantees input-to-state stability (ISS), improving upon existing results that yield only practical ISS or lack explicit data-rate conditions. Simulation results illustrate the effectiveness of the strategy.