Bibliographic record
Abstract
A hybrid system is in essence a combination of continuous dynamical system and discrete event systems that exhibit simultaneously several kinds of dynamic behavior. Although hybrid systems have become popular, their use in such applications as physical, chemical, and control systems is vulnerable to time delays which often lead to instability. Consequently, this thesis is to investigate the stability problems of hybrid systems with time delay. It mainly covers switched delay systems, impulsive delay systems and impulsive neutral systems. In this thesis, Lyapunov function method and inequality techniques are applied to switched delay systems. It is shown that slowly switched stable systems is stable. Then, the results are extended to systems that include their stable and unstable subsystems. Some relations of the dwell times among the stable subsystems and unstable subsystems, based on the inequalities, are derived to guarantee stability. Impulsive delay systems and large scale impulsive delay systems are then investigated, resulting in some sufficient conditions for stability. It is demonstrated that when the system matrix is unstable, time delay and impulses can stabilize the system. By developing some new inequalities, the relations among the delay, impulses, and system matrices are given. Furthermore, absolute stability, based on Lyapunov functional, are studied for some impulsive delay systems. Conditions for the system matrix are developed so that impulsive delay systems are absolutely stable. Neutral impulsive systems are also studied. The emphasis is on the sufficient conditions which guarantee that the large scale neutral impulsive system is stable. After establishing some inequalities, the results on their stability are developed for neutral impulsive systems. Finally, applications to Internet congestion control and impulsive control system are discussed.
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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 | 0.000 | 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)
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".