Stability Criterion for General Proper Systems with Constrained Control Structure
Bibliographic record
Abstract
The focus of this paper is directed towards decentralized stabilizability of interconnected systems. It is assumed that the modes of the system are nonzero and distinct. The notion of quotient fixed mode (QFM), which was introduced in the literature for the class of strictly proper systems, is extended to comprise the class of general proper systems. It is to be noted that this extension is not trivial at all, even for simple two-input two-output systems. It is then shown that a mode of the system is fixed by means of any type of decentralized control law (i.e., nonlinear and time-varying) if and only if it is a QFM of the system. Two different approaches are proposed to determine the QFMs of a system, each one having its own advantages. It is also proved that any distinct and nonzero mode which is not a QFM, can be eliminated by means of sampling. Then, the important problem of placing all modes of the system simultaneously at some desired locations is discussed and an efficient procedure is given to solve it accordingly. A numerical example is presented to thoroughly illustrate the underlying 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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.003 | 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".