Discontinuities and hysteresis in quantized average consensus

We consider continuous-time average consensus dynamics in which the agents’ states are communicated through uniform quantizers. Solutions to the resulting system are defined in the Krasowskii sense and are proven to converge to conditions of “practical consensus”. To cope with undesired chattering phenomena we introduce a hysteretic quantizer, and we study the convergence properties of the resulting dynamics by a hybrid system approach.

💡 Research Summary

The paper investigates continuous‑time average consensus when the agents exchange their states through uniform quantizers, a situation that naturally arises in digital communication networks. Because quantization introduces discontinuities, the resulting closed‑loop dynamics cannot be described by ordinary differential equations in the classical sense. To address this, the authors adopt the Krasovskii differential inclusion framework, which replaces the discontinuous quantizer with its set‑valued Krasovskii regularization. This yields a well‑posed set‑valued differential equation (\dot{x}\in -L\mathcal{K}