A Necessary and Sufficient Condition for the Existence of a LTI Stabilizing Decentralized Overlapping Controller
Bibliographic record
Abstract
This paper deals with the stability of the large-scale interconnected systems with a constrained control structure. It is assumed that the information flow matrix for the interconnected control system is given. This matrix determines which outputs of the system are available for constructing any input signal of the system. The notion of decentralized overlapping fixed mode (DOFM) is introduced, and it is shown that those modes of the system which are not DOFM, can be freely placed anywhere in the complex plane, by means of a linear time-invariant (LTI) structurally constrained controller. This implies that the system is stabilizable by a LTI structurally constrained controller, if and only if it does not have any unstable DOFM. Furthermore, a design procedure is proposed to obtain a stabilizing controller for the systems with no unstable DOFM. In addition, the problem of optimal LTI structurally constrained control design with respect to a quadratic performance index is discussed. The numerical examples given demonstrate the effectiveness of the proposed method
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 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) | 0.006 | 0.001 |
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".