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arxiv: 2604.10596 · v1 · submitted 2026-04-12 · 📡 eess.SY · cs.SY

Distributed Observers with Dynamic Event-Triggered Communication

Yiyang Liu , Xianwei Li , Shaoyuan Li This is my paper

Pith reviewed 2026-05-10 16:25 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords distributed observersdynamic event-triggeringminimum inter-event timeZeno behaviorexponential convergencelinear systemsstate estimationnode-based and edge-based triggers
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The pith

Dynamic event-triggered distributed observers for linear systems enforce strictly positive minimum inter-event times while driving estimation errors to zero exponentially.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The work examines distributed state estimation for linear time-invariant plants when sensors exchange data only at discrete event instants rather than continuously. Static event rules often risk Zeno behavior, in which events accumulate infinitely in finite time and render the scheme unrealizable. The authors introduce dynamic event triggers that incorporate internal comparison functions to adjust the threshold over time. They prove that both node-wise and edge-wise versions of these triggers maintain a strictly positive lower bound on the time between any two events and still guarantee exponential decay of the collective estimation error. Numerical cases confirm that the design cuts communication volume while preserving the desired convergence.

Core claim

The proposed dynamic event-triggered distributed observer, constructed with new comparison functions inside the triggering condition, guarantees that the minimum inter-event time remains strictly positive for both node-based and edge-based mechanisms and that the distributed estimation error converges to zero exponentially for any linear time-invariant system.

What carries the argument

Dynamic event-triggering law augmented by comparison functions that evolve an internal variable to raise the triggering threshold and thereby enforce a positive dwell time between communications.

If this is right

  • Both node-based and edge-based dynamic triggers become viable for distributed observers without Zeno behavior.
  • Exponential convergence of the estimation error holds under the same Lyapunov-type conditions used for continuous communication.
  • Average communication rate drops compared with periodic or static event schemes while stability margins are retained.
  • The design applies directly to networks of sensors estimating a common LTI state vector.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same comparison-function technique might be adapted to obtain positive inter-event times for nonlinear or switched observers if suitable bounding functions can be derived.
  • Coupling the observer with an event-triggered controller could yield a fully event-based closed-loop architecture with guaranteed positive dwell times.
  • Large-scale network simulations could test whether the positive-MIET bound degrades with network size or communication delays.

Load-bearing premise

The comparison functions and trigger parameters can be selected so that the resulting inter-event intervals stay bounded away from zero while the observer error system remains exponentially stable.

What would settle it

A concrete linear system, observer gain matrix, and set of comparison functions for which the simulated inter-event times approach zero or the estimation error norm fails to decay exponentially.

Figures

Figures reproduced from arXiv: 2604.10596 by Shaoyuan Li, Xianwei Li, Yiyang Liu.

Figure 1
Figure 1. Figure 1: The communication graph among agents. In this section, we use numerical examples from [9] to il￾lustrate the effectiveness of our approach. Specifically, a three-inertia system is considered, which is observed by four agents. The communication topology among agents is represented by an undirected graph, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Triggering function of observer 1 over 0 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Event intervals τ i k, k ∈ N, for each agent. The dash and dotted lines together with the corresponding numbers indicate the mean and minimum of τ i k over k, respectively. The horizontal and vertical coordinates of each circle “◦” are the event instants and event intervals, respectively. 10-2 10-1 100 101 102 103 0 0.02 0.04 0.06 0.08 0.1 0.12 10-2 10-1 100 101 102 103 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 … view at source ↗
Figure 5
Figure 5. Figure 5: Guaranteed level τ i , mink{τ i k} and meank{τ i k} for different κ0. meank{τ i k } denote the minimum and the average of the sequence {τ i k }, respectively. As can be seen from [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
read the original abstract

This paper studies the problem of distributed state estimation of linear time-invariant (LTI) systems under event-triggered communication. For event-triggering mechanisms, the existence of positive minimum inter-event times (MIETs) is an essential property for ensuring practicality. It is widely recognized that dynamic event-triggering mechanisms can effectively reduce redundant communication. However, for distributed observers, it remains unclear whether dynamic event-triggering mechanisms can ensure positive MIETs. This paper proposes a dynamic event-triggered distributed observer. By introducing new comparison functions, it is proven that the dynamic event-triggered distributed observer can guarantee strictly positive MIETs and ensure the exponential convergence of the estimation error. Moreover, most existing works on event-triggered distributed observers only consider node-based event-triggering mechanisms, while both node-based and edge-based dynamic event-triggering mechanisms are constructed in this paper. Numerical examples are provided to illustrate the effectiveness of the proposed results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. This paper studies distributed state estimation for linear time-invariant systems under event-triggered communication. It proposes both node-based and edge-based dynamic event-triggered distributed observers and introduces new comparison functions to prove that these mechanisms guarantee strictly positive minimum inter-event times (MIETs) while ensuring exponential convergence of the estimation errors.

Significance. If the central claims hold, the work is significant for practical multi-agent estimation because positive MIETs prevent Zeno behavior, a common obstacle in event-triggered designs. The extension to edge-based dynamic triggering and the use of tailored comparison functions to bound inter-event times provide a concrete technical route that aligns with and extends existing literature on dynamic event-triggering for distributed observers.

minor comments (2)
  1. The abstract states that new comparison functions are introduced to prove positive MIETs, but the manuscript should explicitly state the minimal assumptions on system observability, graph connectivity, and the choice of design parameters that make the comparison functions feasible (e.g., in the stability and MIET analysis sections).
  2. Numerical examples are mentioned to illustrate effectiveness; the manuscript would benefit from reporting the specific parameter values used for the dynamic triggering thresholds and comparison functions so that the positive MIET property can be directly verified from the simulations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work and the recommendation for minor revision. The assessment correctly highlights the significance of guaranteeing strictly positive MIETs via dynamic event-triggering for both node-based and edge-based distributed observers, along with the use of tailored comparison functions to establish exponential convergence.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives positive MIETs and exponential error convergence by introducing new comparison functions into the dynamic event-triggered observer analysis. This step applies standard comparison lemmas to the augmented error dynamics and does not reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations. The node- and edge-based mechanisms are constructed explicitly, with the MIET lower bound obtained independently via the new functions rather than renamed from prior results. The derivation remains self-contained and consistent with external event-triggered control techniques.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions for distributed observers (detectability of the LTI system and connectivity of the communication graph) plus the novel comparison functions introduced in the paper; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The underlying LTI system is detectable and the communication graph is connected.
    Required for any distributed observer to achieve consensus on the state estimate; standard in the field but not explicitly listed in the abstract.

pith-pipeline@v0.9.0 · 5454 in / 1112 out tokens · 62407 ms · 2026-05-10T16:25:21.087773+00:00 · methodology

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