A necessary and sufficient condition for stabilization of decentralized time-delay systems with commensurate delays
Bibliographic record
Abstract
This paper investigates the stabilization problem for interconnected linear time-invariant (LTI) time-delay systems by means of linear time-invariant output feedback decentralized controllers. The delays are assumed to be commensurate and can appear in the states, inputs, and outputs of the system. First, the canonical forms for this type of time-delay systems are introduced and centralized fixed modes (CFM) for this type of systems are defined. It is then shown that a time-delay system which is both controllable and observable does not have any CFMs. Furthermore, an efficient technique for characterizing CFMs of any LTI time-delay system with commensurate delays is obtained. Decentralized fixed modes (DFM) are then defined accordingly, and a necessary and sufficient condition for decentralized stabilizability of the interconnected time-delay systems is proposed. Finally, a numerical example is given to illustrate the importance of results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".