A new method for the stability robustness determination of state space models with real perturbations
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Bibliographic record
Abstract
The authors consider the robust stability of a linear time-invariant state-space model subject to real plant data perturbations. The problem is to find the distance of a given stable matrix from the set of unstable matrices. A novel method, based on the properties of Kronecker product and two other composite matrices, is developed to achieve this aim: The method makes it possible to distinguish real perturbations from complex ones. Explicit bounds on the distance of a stable matrix from the set of unstable matrices are obtained for both the continuous-time and discrete-time case. The bounds are applicable only for the case of real plant perturbations; hence they are less conservative to apply than for the case when complex perturbations are allowed. Several examples are given to demonstrate the new bounds, which in general are shown to be tighter than results previously reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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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 | 0.000 | 0.000 |
| 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 it