On stability robustness of discrete-time systems: the complex-variable approach of Mastorakis
Bibliographic record
Abstract
The key element of Mastorakis' approach is the well-known theorem of Rouche: Suppose f(z) and d(z) are analytic in domain D and on its simple closed boundary /spl part/D, and suppose that |d(z)|<|f(z)| on /spl part/D. Then f(z) and f(z)+d(z) have the same number of zeros in D. By taking the nominal and perturbed denominator polynomials of a stable discrete-time transfer function as f(z) and f(z)+d(z), respectively, and taking the unit disk as D, Rouche's theorem is directly connected to a stability-robustness study. This paper proposes an enhanced complex-variable approach initiated by Mastorakis to derive several improved bounds for stable coefficient perturbations of a nominal Schur polynomial.
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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 | 0.000 | 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) | 0.001 | 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".