Worst-case asymptotic properties of ℋ∞ identification

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