Convergence properties in H_infinity identification with approximated models

摘要

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_infinity approximation of the system withina given class of parametric models, which may not include the unknown system. An estimation algorithm is given, requiring the solution of two linear programming problems. A bound on its worst-case H_infinity error is derived and it is estimated how far it is from being optimal. Asymptotic properties of the estimated mdoela re derived under suitable conditions on input. Roughly speaking, these asymptotic results show that, for finite values of the measurement error bound, estimated models can be obtained, which with probability 1 are asymptotically as near as desired to the best H_infinity approximation of the unknown system.