Passive linear time-varying systems: State-space realizations, stability in feedback, and controller synthesis
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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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 | 0.000 | 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".