Asymptotic stability of piecewise affine systems with sampled-data piecewise linear controllers
Bibliographic record
Abstract
This paper addresses stability analysis of closed-loop sampled-data piecewise affine (PWA) systems. In particular, we study the case in which a PWA plant is in feedback with a sampled-data piecewise linear (PWL) controller. We consider the sampled-data system as a continuous-time system with a variable time delay. The contributions of this work are threefold. First, we present a modified Lyapunov-Krasovskii functional (LKF) for studying PWA systems with time delay. Second, based on the new LKF, sufficient conditions are provided for asymptotic stability of PWA systems in feedback with sampled-data PWL controllers. Finally, following the time-delay approach, we formulate the problem of finding a lower bound on the maximum delay that preserves asymptotic stability to the origin as an optimization program in terms of LMIs. The new results are successfully applied to a unicycle example.
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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 | 0.001 | 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 | 0.001 | 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 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".