A fixed-time inverse-free dynamical system for solving the system of absolute value equations

Xuehua Li, Dongmei Yu, Yinong Yang, Deren Han, Cairong Chen

incompletemedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s fixed-time stability result and constants match a correct Lyapunov derivation, and the model reproduces essentially the same inequalities and fixed-time bound. However, both mishandle well-posedness: the vector field f(x)=ρ(x)g(γ,x) is not locally Lipschitz at r(x)=0 when λ1∈(0,1), so the paper’s claim of global uniqueness (Theorem 3.2) is unjustified, and the model’s claim that post-hitting continuation is uniquely constant is also not generally valid. The fixed-time Lyapunov proof is otherwise sound.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The main fixed-time Lyapunov derivation is correct and the constants are explicit and useful; the contribution is a solid, specialized note extending inverse-free AVE dynamics with a fixed-time gain. However, the well-posedness part is incorrect: global uniqueness is asserted without controlling the non-Lipschitz factor ρ(·) at the equilibrium. This should be repaired by framing solutions in the Carathéodory sense and clarifying uniqueness away from r=0, which does not affect the fixed-time result.