Extension of generalized KYP lemma: from LTI systems to LPV systems

Jingjing Zhang, Jan Heiland, Peter Benner, Xin Du

incompletehigh confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:57 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate solution reproduces the paper’s intended dissipativity proof for the extended gKYP condition (Theorem 2) essentially verbatim, using the Ω_{f+δ}-IQC from Theorem 1 to eliminate the Ψ-term and conclude the input–output performance bound. However, both the paper and the candidate omit a needed technical condition: handling the boundary term V(x(∞),∞) = x(∞)^*P(p(∞))x(∞). The paper integrates directly over [0,∞) and asserts ≤ 0 without explicitly requiring UAS (to ensure x(t)→0) or P≽0; the candidate similarly claims a finite-horizon inequality and invokes V(T)→0 under merely BIBS+L2, which is not guaranteed. Aside from this gap, the proofs match closely.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper proposes a practical and conceptually clean extension of gKYP-style analysis to LPV systems under finite-frequency excitation via an enlarged-range IQC. The construction of Ω\_{f+δ} tied to a pole-range gap and finite-frequency Gramians is compelling and well-motivated, and the main LMI result is valuable for applications. The proof of the performance theorem, however, omits an explicit assumption required to eliminate the terminal energy term; adding UAS (or P ≽ 0) would close this gap. With this minor fix and a clearer discussion of infinite- vs. finite-horizon IQCs, the paper meets standards for a solid contribution.