A Necessary and Sufficient Condition for the Existence of a LTI Stabilizing Decentralized Overlapping Controller
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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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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