Robust Stability and Robust Stabilizability
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Most real systems cannot be represented by linear dynamics, but sometimes, under some assumptions, it is possible to model the dynamical behavior of practical systems with a linear model having some uncertainties. The presence of these uncertainties in the dynamics requires the establishment of robust conditions that can guarantee the stability and/or the stabilizability of the practical system under study. This topic has in fact dominated the research effort of the control community during the last two decades. Among the contribution on this area of research we quote the work of [77, 105, 114] on robust stability and the work of [49, 108, 110, 118, 128, 155, 189, 190, 206, 207, 215] on robust stabilizability. This chapter will deal with the robust stability and robust stabilizability of the class of uncertain continuous-time linear time delay systems. Our results are mainly based on the Lyapunov second method. In some sense, given an uncertain dynamical system with time delay, we answer the following questions: How can we check whether the unforced nominal system with time delay is stable or not?How can we check if the unforced uncertain dynamical system with time delay is robust stable for all admissible uncertainties or not?When the unforced uncertain dynamical system with time delay is unstable, how can we design a memoryless state feedback, or memory state feedback or output feedback controller to stabilize the system and guarantee that it will remain stable for all admissible uncertainties?
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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