Impulse Controllability: From Descriptor Systems to Higher Order DAEs
Bibliographic record
Abstract
Impulsive solutions in LTI dynamical systems have received ample attention, but primarily for descriptor systems, i.e., first order Differential Algebraic Equations (DAEs). This paper focuses on the impulsive behavior of higher order dynamical systems and analyzes the causes of impulses in the context of interconnection of one or more dynamical systems. We extend the definition of impulse-controllability to the higher order case. Amongst the various nonequivalent notions of impulse-controllability for first order systems available in the literature, which mostly rely on the input/output structure of the system, our definition, based on a so-called state-map obtained directly from the system equations, generalizes many key first order results to the higher order case. In particular, we show that our higher-order-extension of the definition of impulse controllability generalizes the equivalence between impulse controllability and the ability to eliminate impulses in the closed loop by interconnecting with a suitable controller. This requires an extension of the definition of regularity of interconnection from behaviors involving only smooth trajectories to behaviors on the positive half line involving impulsive-smooth trajectories.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 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 | 0.001 |
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".