MAPPING DISCRETE-TIME MODELS FOR DESCRIPTOR-SYSTEMS WITH CONSISTENT INITIAL CONDITIONS
Bibliographic record
Abstract
Discretization of a regular continuous-time descriptor-system, whose initial condition is consistent with its input, is considered using a general mapping method presented in our previous paper. The proposed mapping discrete-time model is shown to be a proper discretization under the definition explained in the paper. This assures that the response of the mapping model approaches that of the continuous-time descriptor system as the sampling period approaches zero. The consistency of initial conditions for the discrete-time model is also studied and the long-standing issue of ambiguities surrounding irregularities of discrete-time responses at the initial time are clarified with a simple solution. A proper range of design parameters are investigated and their suitable choices suggested. To illustrate the use of the proposed method, a simple circuit that cannot be expressed in the ordinary state-space form is considered. Its responses to a sinusoidal input when started from the consistent and inconsistent initial conditions are simulated to show that the irregularities at the initial time can be overcome easily. The proposed technique provides a convenient simulation and design environment for handling discrete-time systems in a unified manner with consistency and ease.
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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 | 0.001 | 0.002 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".