Conditions for stabilizability of time‐delay systems with real‐rooted plant
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Bibliographic record
Abstract
Abstract In this article we consider the ‐stabilization of n th‐order linear time‐invariant dynamical systems using multiplicity‐induced‐dominancy ‐based controller design in the presence of delays in the input or the output channels. A sufficient condition is given for the dominancy of a real root with multiplicity at least and at least n using an integral factorization of the corresponding characteristic function. A necessary condition for ‐stabilizability is analyzed utilizing the property that the derivative of a ‐stable quasipolynomial is also ‐stable under certain conditions. Sufficient and necessary conditions are given for systems with real‐rooted open‐loop characteristic function: the delay intervals are determined where the conditions for dominancy and ‐stabilizability are satisfied. The efficiency of the proposed controller design is shown in the case of a multilink inverted pendulum.
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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 | 0.000 |
| 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)
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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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