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Worst-case asymptotic properties of ℋ identification

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2 Author(s)
Jie Chen ; Dept. of Electr. Eng., California Univ., Riverside, CA, USA ; Guoxiang Gu

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

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:49 ,  Issue: 4 )