Design of sliding observers for Lipschitz nonlinear system using a new time-averaged Lyapunov function
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Bibliographic record
Abstract
This paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of Gaussian input disturbances and sensor noises. The paper first proposes a novel candidate for Lyapunov stability, termed a Time-averaged Lyapunov (TAL) function. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbance. The paper then provides the necessary and sufficient condition for the design of the sliding observer gainsusing the TAL in the form of Linear Matrix Inequality (LMI). The LMIs can then be explicitly solved offline using commercial LMI solvers. The paper compares the LMIs for the two observer designs to demonstrate the design of the sliding mode observer using TAL can greatly enhance the scope of observer design for nonlinear systems.
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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 | 0.001 | 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