Title
Worst-case asymptotic properties of H∞ identification
Document Type
Article
Publication Date
4-1-2002
Abstract
This paper studies asymptotic properties of H∞ identification problems and algorithms. The sample complexity of time- and frequency-domain H∞ identification problems is estimated, which exhibits a polynomial growth requirement on the input observation duration for the time-domain H∞ identification problem, and a linear growth rate of frequency response samples required for the frequency-domain H∞ identification problem. The divergence behavior is also established for linear algorithms for the time- and frequency-domain problems. The results extend previous work to more restricted sets of linear time-invariant systems with more refined a priori information, specifically imposed on the stability degree and the steady-state gain of the systems, thus demonstrating that no robustly convergent linear algorithms can exist even for a small set of exponentially stable systems.
Publication Source (Journal or Book title)
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
First Page
437
Last Page
446
Recommended Citation
Chen, J., & Gu, O. (2002). Worst-case asymptotic properties of H∞ identification. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49 (4), 437-446. https://doi.org/10.1109/81.995658