MATLAB tools for linear and nonlinear system stability theorem implementation
Bibliographic record
Abstract
Three MATLAB-based tools have been developed for the convenient assessment of stability conditions for linear and nonlinear systems. The first is a more helpful and definitive version of Nyquist, which has features of automatic zooming (to show all crossings of the real axis and thus display the corresponding critical gain points) and which displays on the real axis a numeral ('0', '1', etc.) that represents the number of unstable (right-half plane) poles that will occur in a closed-loop system with feedback gain k if the point -1/k is located in that region. The second tool is built on this extended Nyquist command, and makes the application of the nonlinear time-varying system circle criterion equally simple and definitive. Finally, a Popov criterion tool is included to achieve better sector bounds for the nonlinear time-invariant case. Examples are presented to show the efficacy of these extensions within the MATLAB environment.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.117 | 0.063 |
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 source (direct Gemma or distilled Codex), 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".