Observer design for generalized sector-bounded noisy nonlinear systems
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Bibliographic record
Abstract
This article presents a new observer for a class of nonlinear systems, defined as a “generalized sector-bounded” nonlinear system, in the presence of both sensor and input disturbances. The generalized sector-bounded nonlinearity is shown to be a super-set of Lipschitz, bounded Jacobian, one-sided Lipschitz, monotonically increasing and dissipative nonlinearities. This article presents necessary and sufficient conditions for this observer to guarantee a desired minimum performance. The conditions for the observer are presented as a linear matrix inequality that can be solved offline using commercial solvers, and the solution to the linear matrix inequality is used to explicitly compute the observer gain. This article then extends these results to case where an additive nonlinearity appears in the sensor output. The use of the methodology developed in this article is demonstrated through illustrative examples. Compared to previous results on nonlinear observers, the proposed observer guarantees a global performance measure for a very general class of nonlinear systems and does not require online computation of the observer gain.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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