Exponential stability of impulsive systems with complex delays: impulsive control and its application
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
This paper investigates the exponential stabilisation problem of nonlinear impulsive systems with complex delays, in which both system and impulse delays are permitted to exceed impulse intervals. These complex delays induce intricate dependencies between system states and control actions, significantly increasing difficulty in deriving sufficient conditions for global exponential stability (GES). To tackle this challenge, a novel interval partitioning analysis method is presented. It establishes a quantifiable relationship between impulse delay, impulse interval, and system state. Building on this relationship, a new Razumikhin inequality is designed, leveraging the influence of impulse delay on system stability and eliminating the constraints between impulse and system delays. By using the average dwell time (ADT) criterion, a sufficient stability condition expressed as Linear Matrix Inequalities (LMIs) is derived. It is shown that under specific conditions on the historical state feedback and impulse sequence, the delayed impulse system exhibits exponential stability, even with variable impulse intervals. Two numerical examples demonstrate the effectiveness of the presented method, showcasing its applicability to image encryption.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it