Source-linked AI summary
Comment on "Event-Triggered Stabilization of Linear Time-Delay Systems via Halanay-Type Inequality"
Luke Jonker, Kexue Zhang
TL;DR
The comment addresses technical gaps in the proof of Lemma 1 from, which underpins an event-triggered stabilization analysis. It supplies a corrected argument retaining the exponentially decaying term, while preserving the lemma’s original statement.
Problem
The proof of Lemma 1 in contains technical gaps in its estimate and contradiction argument, motivating clarification of the lemma’s proof.
Method
The comment establishes the estimate through a corrected argument that avoids both identified issues while retaining the exponentially decaying term.
Results
The statement of the original lemma remains valid, with the convergence decay rate determined by the minimum of the characteristic decay rate and the exponential term’s decay rate.
Takeaways & Limitations
Careful retention of the exponentially decaying term is essential for the resulting convergence estimate.
Takeaways & Limitations
The comment is limited to correcting technical issues in the proof of Lemma 1, including an invalid contradiction argument based on insufficient monotonicity.
Abstract
from arXiv · showhide
This comment revisits Lemma 1 in [1], which plays a central role in the event-triggered stabilization analysis developed therein. We identify technical gaps in the proof of the lemma and provide a corrected argument. In particular, careful treatment of the exponentially decaying term shows that its decay rate must be retained in the resulting convergence estimate. The statement of the original lemma, with the exponential decay rate determined by the minimum of the characteristic decay rate and the decay rate of this term, remains valid.