Inputs for convergent SM identification with approximated models

In the paper the following problem is studied: input-output measurements of a linear time-invariant discrete-time exponentially stable system are available, corrupted by a bounded stochastic noise with finite probability density function at the boundary, and it is desired to identify the best H_∞ approximation of the system within a given class of parametric models, which may not include the unknown system. In a previous paper convergence results have been presented without requiring the noise level to go to zero. These results are related to a suitable excitation property of the input signal called persistent performance. In this paper it is shown that some typical inputs used in identification achieve such a property