Restricted real perturbation values with applications to the structured real controllability radius of LTI systems
Bibliographic record
Abstract
In this paper, the concept of restricted real perturbation values of a complex matrix triplet is introduced, and a formula for computing lower bounds of these values is presented. Restricted real perturbation values are a generalization of the real perturbation values introduced in, which is a key concept in evaluating various robustness radii found in the control literature, such as the real controllability/observability radius, the real decentralized fixed-mode radius, the real minimum-phase radius, etc. The generalization to restricted real perturbation values is needed for an extension of these radii to account for more general system perturbation structures. As an example, we used the results of this paper to compute the true value of the structured real controllability radius of the multi-link inverted pendulum system. Also, we numerically investigate cases of when the provided lower bounds are achievable.
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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) | 0.000 | 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".