Decentralized fixed modes for LTI time-delay systems
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Bibliographic record
Abstract
This paper investigates the stabilization problem for a linear time-invariant (LTI) time-delay system by means of a decentralized finite-dimensional LTI output feedback controller. Both commensurate and incommensurate delays are considered. It is assumed that delay can appear in the state, inputs, and outputs of the system. In this case, using the definition of μ-decentralized fixed modes (μ-DFM) introduced in a recent work necessary and sufficient conditions for the decentralized stabilizability of LTI time-delay systems is obtained. Some algebraic conditions are also provided to determine if a mode of a time-delay system is a μ-DFM. A numerical algorithm is proposed to obtain the set of μ-DFMs of the system, and the notion of μ-approximate decentralized fixed modes (μ-ADFM) is also presented. Finally, three numerical examples are given to illustrate various applications of the 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