Analysis of Sliding Mode Observers Using a Novel Time-Averaged Lyapunov Function
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Bibliographic record
Abstract
Sliding mode observers are known to be robust to model uncertainties. However, sliding mode observers have not been well analyzed in the presence of Gaussian disturbances and no previous results exist for a pure sliding mode observer in the presence of sensor noise. A traditional quadratic Lyapunov function that is used to determine the stability of sliding mode observers, fails for noisy systems. Hence this paper introduces a novel Lyapunov candidate function termed the time averaged Lyapunov (TAL) function to analyze the stability of noisy systems. The TAL specifically examines the effect of the Gaussian noise on a sliding mode observer. Using this TAL function, the paper demonstrates that Gaussian sensor noise does not affect the stability or chatter of the observer. Further, the covariance of the noise only affects the convergence rate of the observer. Simulation results are reported to demonstrate the effectiveness of the proposed approach on a Linear system.
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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 | 0.000 | 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 it