The Intrinsic State Variable in Fundamental Lemma and Its Use in Stability Design for Data-based Control

Yitao Yan, Jie Bao, Biao Huang

correcthigh confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves that the SVD-based parameterizer g in w̃k = F gk is an intrinsic, observable state (Theorem 3, gk = F† w̃k, and overlap Fp gk = Πp F gk−1) and then derives an LMI condition for memoryless stabilization with the controller uk = Πu F(F†p Πp F + Fz Y W−1)gk−1 (Theorem 6). The candidate solution follows the same constructions and Schur-complement/Lyapunov arguments with A := F†p Πp F, yielding the identical LMI [ W * ; AW + Fz Y W ] ≻ 0 and the same control law, hence they are essentially the same proof with notational reshuffling.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

This work reframes the Hankel-parameterizer from Willems’ fundamental lemma as an intrinsic, observable state, enabling a compact LMI-based stabilization procedure directly from data. The logical flow (state property via window overlap; observability via full-column-rank SVD; stabilization via memoryless Lyapunov and Schur complement) is coherent and correct, and the controller is explicit. Clarifying standing assumptions (lag/rank) and some linear-algebra steps (kernel parametrization, weaving) would further strengthen accessibility and reproducibility.