2507.22243
MODIFIED SMITH PREDICTOR FOR UNSTABLE LINEAR SYSTEMS
A. A. PYRKIN, K. YU. KALININ
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves global exponential stability for the modified Smith predictor with periodic integrator resets without requiring A to be Hurwitz, carefully accounting for the delayed jump in z at t = mT + D. The candidate solution incorrectly assumes A must be Hurwitz and models the flows as a single LTI segment per period, ignoring the essential z jump at t = mT + D; its Lyapunov contraction over a full period is therefore invalid.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper proposes a simple and implementable modification of the Smith predictor that achieves global exponential stabilization for delayed LTI plants, including unstable ones, via a periodic reset of an auxiliary integrator. The analysis is technically sound, exploiting a discrete-time inequality at delayed jump instants. A minor sign typo appears in an intermediate lemma, and some derivations are concise; clarifying these points would further strengthen readability. Overall, the contribution is well-motivated and correct, with clear potential impact for delayed-system control.