Exponential stability of impulsive systems with complex delays: impulsive control and its application
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".