Finite‐Time Input‐To‐State Stability for Infinite‐Dimensional Systems
Bibliographic record
Abstract
ABSTRACT In this paper, we extend the notion of finite‐time input‐to‐state stability (FTISS) for finite‐dimensional systems to infinite‐dimensional systems. More specifically, we first prove an FTISS Lyapunov theorem for a class of infinite‐dimensional systems, namely, the existence of an FTISS Lyapunov functional (FTISS‐LF) implies the FTISS of the system, and then, provide a sufficient condition for ensuring the existence of an FTISS‐LF for a class of abstract infinite‐dimensional systems under the framework of compact semigroup theory and Hilbert spaces. As an application of the FTISS Lyapunov theorem, we verify the FTISS for a class of parabolic PDEs involving sublinear terms and distributed in‐domain disturbances. Since the non‐linear terms of the corresponding abstract system are not Lipschitz continuous, the well‐posedness is proved based on the application of compact semigroup theory, and the FTISS is assessed by using the Lyapunov method with the aid of an interpolation inequality. Numerical simulations are conducted to confirm the theoretical results.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".