Möbius transformation and application to coupled stability analysis of cascaded master and slave networks
Bibliographic record
Abstract
In this paper, we use the notion of Möbius transformation to develop a chain stability analysis methodology to verify the coupled stability of master-slave teleoperation systems modeled by a cascade of networks. The methodology tracks the transmitted passivity unit disk of the load through the cascade to the user network and provides less restrictive stability conditions compared to having passive or absolutely stable networks. Since the Möbius analysis is decentralized, as opposed to other existing methods such as Llewellyns, the proposed methodology is more suitable for dynamic distributed systems in which a network block in the cascade is modified, added or taken out. We further introduce the notion of “bounded-G absolute stability” to verify the coupled stability for any prescribed range of loads, denoted by circles in the scattering domain. To show the effectiveness of the method numerical analysis and simulation results of a force-position teleoperation system under constant time delay are provided.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".