Stability and stabilization of piecewise‐affine slab systems subject to Wiener process noise
Bibliographic record
Abstract
Summary The main contribution of this paper is to propose a convex formulation of sufficient conditions for both stability analysis and synthesis of stabilizing controllers for stochastic piecewise affine (PWA) systems with multiplicative noise. One of the main difficulties in PWA systems is the fact that the affine terms in the dynamics make it extremely difficult to formulate the synthesis problem as a convex optimization or even convex feasibility program. The presence of multiplicative noise modeled as a Wiener process adds an additional level of difficulty to the analysis and synthesis procedures. Sufficient conditions for stability of stochastic PWA slab systems in the mean square sense are developed first using a stochastic globally quadratic Lyapunov function. Second, PWA state feedback controllers are designed such that the closed‐loop system is stochastically exponentially mean square stable. The conditions for both stability and stabilization are formulated as LMIs, which can then be solved efficiently using currently available software packages. A numerical example shows the effectiveness of the approach. Copyright © 2013 John Wiley & Sons, Ltd.
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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