Passive linear time-varying systems: State-space realizations, stability in feedback, and controller synthesis
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Bibliographic record
Abstract
In this paper we consider linear time-varying passive systems. We state various theorems, which rely on the state-space matrices of the system, that identify when a linear-time varying system is purely passive, input strictly passive, output strictly passive, or input-state strictly passive which is a nonstandard notion of passivity defined in this paper. Two of our theorems resemble the Kalman-Yakubovich- Popov Lemma, one applicable to time-varying systems with a feedthrough matrix and the other for linear time-varying systems without one. The negative feedback interconnection of various systems is considered. We show that an output strictly passive system negatively interconnected with an input-state strictly passive system is globally asymptotically stable. We also show that both linear time-varying input-state and output strictly passive systems when connected in negative feedback with a sector bounded, memoryless nonlinearity are also globally asymptotically stable. The optimal design of a time-varying output strictly passive controller is also considered. We present an example: the position and velocity control of a time-varying mass controlled via a dynamic time-varying compensator and a sector bounded, memoryless nonlinearity.
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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 | 0.001 |
| 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