Stability Analysis of Delayed Discrete Singular Piecewise Homogeneous Markovian Jump Systems With Unknown Transition Probabilities via Sliding-Mode Approach
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Bibliographic record
Abstract
In this article, the sliding-mode control (SMC) strategy is outlined for discrete-time singular Markovian jump systems with time-varying delays and time-varying transition probabilities (TPs). To simplify the complexities arising from the time-varying TPs in the Markov chain, the TPs in this study are reasonably considered to be finite piecewise-homogeneous. The variations of TPs are stochastic and governed by a higher level transition probability (HTP) matrix. It is acceptable for both the TP matrix and HTP matrix to be partly unknown, which makes the system closer to reality and more complex to investigate. In this context, our goal lies in constructing a common sliding-mode surface to avoid the effects of switching among sequential subsystems and piecewise homogeneous TPs on the convergence of the sliding-mode surface. Additionally, we aim to design an appropriate SMC law to guarantee the reachability of the quasi-sliding mode in a finite-time interval. Through the linear matrix inequalities, sufficient criteria are offered to make the closed-loop dynamic system stochastically admissible. Finally, the numerical result will show that the presented SMC strategy is valid.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| 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