2103.01397
Finite time Convergence of Pinning Synchronization with Linear and Nonlinear Controllers
Wenlian Lu, Xiwei Liu, Tianping Chen
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 1 claims finite-time pinning under c0·θ > L for positive diagonal Γ, but its own proof actually requires c0·θ·γ_min > L (γ_min is the smallest diagonal of Γ). This missing γ_min factor is a substantive omission, and the handling of the discontinuous normalized controller is not fully rigorous. The model’s solution supplies the missing γ_min, uses a correct Dini-derivative/subgradient argument for the l1 norm, and yields a valid finite-time result with an explicit time bound.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper presents a simple and effective finite-time pinning framework for directed networks. The approach is technically sound and practically relevant, but Theorem 1 (and related places) omit a necessary factor involving the smallest diagonal entry of Γ, and the non-smooth analysis is not explicitly handled in the theorem’s proof. These issues can be corrected with minor textual and technical clarifications.