Hybrid passivity and finite gain stability theorem: stability and control of systems possessing passivity violations
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Bibliographic record
Abstract
The stability and control of systems possessing passivity violations is considered. The authors seek to exploit the finite gain characteristics of a plant over a range in which a passive mapping no longer exists while implementing a similar hybrid passive and finite gain controller. Using the dissipative systems framework the authors define a hybrid system: one which possesses a passive map, and finite gain characteristics when the passive map is destroyed. The definition of a hybrid system utilises a switching parameter to break the system into passive and finite gain regions. It is shown that this switching parameter is equivalent to an ideal low-pass filter and can be approximated by a Butterworth filter. The stability of two hybrid systems within a negative feedback interconnection is also considered. A hybrid passivity and finite gain stability theorem is developed using both Lyapunov and input–output techniques, which yield equivalent results. Sufficient conditions for the closed-loop system to be stable are presented, which resemble an amalgamation of the traditional passivity and small-gain theorems.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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