Time-varying state feedback and output injection: duality and distinctions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The classical results on the duality of controllability and observability of linear systems are very well known and deeply analyzed in both cases of time invariant and time-varying linear systems. However the significant difference appears in the important properties of the responses in the problems of stabilization by state feedback (controller) and by output injection (observer) even in cases when only the gains become time-varying. Namely, it is possible to design a time-varying observer with fast decaying error almost without peaking (or equivalently to stabilize the system by output injection providing a fast decay without large deviations). But it is impossible to get the analogous result by using state feedback due to indispensable connection of fast decaying and large peaking. This difference is the main topic of the article and as a motivation for our interest we emphasize that the results of stabilization obtainable by output injection and by state feedback seem to be dual.
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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