Delay-independent decentralized fixed modes for multi-channel LTI systems subject to input and output delays
Bibliographic record
Abstract
This paper concerns stabilizability of a multi-channel linear time-invariant (LTI) system with delay in inputs and outputs by means of a finite-dimensional decentralized output feedback controller. This problem can be tackled by obtaining the set of unstable decentralized fixed modes (DFMs) of the system. Although the set of DFMs for LTI time-delay systems is generally delay-dependent, there exists a certain type of DFMs, which are delay-independent. In this work, the notion of delay-independent DFM (DIDFM) is defined, and algebraic conditions are provided under which a mode of a multi-channel LTI system subject to input and output delays is a DIDFM. The result of this paper is more general than that of [1], due to the fact that that all the modes of the system in [1] are assumed distinct.
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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".