Abstract
AbstractIn this paper we derive the sample complexity for discrete time linear time‐invariant stable systems described in the ℋ︁∞ topology. The problem set‐up is as follows: the ℋ︁∞ norm distance between the unknown real system and a known finitely parameterized family of systems is bounded by a known real number. We can associate, for every feasible real system, a model in the finitely parameterized family that minimizes the ℋ︁∞ distance. The question now arises as to how long a data record is required to identify such a model from noisy input–output data. This question has been addressed in the context of l1, ℋ︁2 and several other topologies, and it has been shown that the sample‐complexity is polynomial. Nevertheless, it turns out that for the ℋ︁∞ topology the sample‐complexity in the worst case can be infinite. Copyright © 2001 John Wiley & Sons, Ltd.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
