Minimal Experiments for Robust Stabilization: Information, Spectral Geometry, and Duration
Abstract
On broad classes of linear systems, the shortest experiments are almost as good as the best possible ones. For n states and m inputs, the shortest input sequences that support robust data-driven stabilization of every controllable plant have mn+1 steps with exact states and m(n+1) with noisy states. We show that, when the spectral radius is bounded and the spectrum is well separated near the unit circle, these sequences tolerate a fixed fraction of the error level achievable by any experiment, even one designed with full plant knowledge and allowed to use any finite duration. This constant-factor comparison can fail for slowly actuated systems. For A=I+hG with controllability depth ν≥2, short experiments lose a factor of order hν−1, and duration of order 1/h is both necessary and sufficient to recover a fixed fraction of the optimal tolerance.
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BibTeX
@misc{peregudin2026minimal,
title = {{Minimal Experiments for Robust Stabilization: Information, Spectral Geometry, and Duration}},
author = {Alexey Peregudin and Ngoc Tuan Dinh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02187},
eprint = {2610.02187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02187},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal Experiments for Robust Stabilization: Information, Spectral Geometry, and Duration
AU - Alexey Peregudin
AU - Ngoc Tuan Dinh
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02187
UR - https://arxiv.org/abs/2610.02187
AB - On broad classes of linear systems, the shortest experiments are almost as good as the best possible ones. For n states and m inputs, the shortest input sequences that support robust data-driven stabilization of every controllable plant have mn+1 steps with exact states and m(n+1) with noisy states. We show that, when the spectral radius is bounded and the spectrum is well separated near the unit circle, these sequences tolerate a fixed fraction of the error level achievable by any experiment, even one designed with full plant knowledge and allowed to use any finite duration. This constant-factor comparison can fail for slowly actuated systems. For A=I+hG with controllability depth ν≥2, short experiments lose a factor of order h^ν−1, and duration of order 1/h is both necessary and sufficient to recover a fixed fraction of the optimal tolerance.
ER -