Generalization of the separation principle beyond constant-gain state-feedback control
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Bibliographic record
Abstract
In the linear control community, the well-known separation principle states that, for a controller designed using an observer and a constant-gain state-feedback gain can be designed separately since the overall closed-loop system eigenvalues are the union of those due to the observer alone and those due to the state-feedback controller alone. In this note, we generalize the separation principle in two directions. First, we use eigenvalue calculations to show that the separation principle holds for dynamic controllers and not just constant-gain controllers; both dynamic state-feedback and dynamic output-feedback controllers are considered. Second, we use a simple linearity argument to argue that the separation principle holds, in fact, not just for the well-known observer structure, but for a whole class of asymptotic observers, including observers that are neither linear nor time-invariant. This paper includes radiotherapy control problem to illustrate the usefulness of these results.
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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