A necessary and sufficient condition for ℋ- index of linear time-varying systems
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Bibliographic record
Abstract
The increasing interests in H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> index leads to some recent development in time domain investigation. This paper presents a necessary and sufficient condition of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> index in a finite time horizon for linear time-varying systems. It shows that the existence of a lower bound of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> index is equivalent to the existence of a certain backward differential Riccati equation. When applied to a linear time-invariant system with infinite time horizon, the result leads to an identical one given in frequency domain study in terms of algebraic Riccati equation. Detailed discussions of the property and special cases are presented. Finally, an example is given to illustrate the main results.
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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.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| 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 |
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