Convergence Analysis of Consensus‑Based Tracking Algorithms for Logical Time Functions in Multi‑Agent Networks

Embedded multi-agent systems often need a shared logical time without a global clock, while requiring that time never goes backwards at any node. We formulate decentralized synchronization as tracking a monotone virtual network time defined by the maximum of agent clocks, and compare three Local Voting Protocol (LVP) variants: average consensus, hard max-tracking, and softmax (log-sum-exp) consensus. Average consensus is structurally mismatched to monotonicity and serves as an ATS-like baseline; max-tracking is monotone but noise-sensitive; softmax smooths aggregation and, with monotonicity enforcement, yields the best steady-state accuracy in simulation. An ESP32 testbed over lossy ESP-NOW links confirms microsecond-level tracking and fast recovery from connectivity disruptions.