Abstract
We study the complexity of worst-case time-domain identification of linear time-invariant systems using model sets consisting of degree-n rational models with poles in a fixed region of the complex plane. For specific noise level δ and tolerance levels τ, the number of required output samples and the total sampling time should be as small as possible. In discrete time, using known fractional covers for certain polynomial spaces (with the same norm), we show that the complexity isO(n 2) for theH ∞ norm,O(n) for the ℓ2 norm, and exponential inn for the ℓ1 norm, for each δ and τ. We also show that these bounds are tight. For the continuous-time case we prove analogous results, and show that the input signals may be compactly supported step functions with equally spaced nodes. We show, however, that the internodal spacing must approach 0 asn increases.
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Harrison, K.J., Partington, J.R. & Ward, J.A. Complexity of identification of linear systems with rational transfer functions. Math. Control Signal Systems 11, 265–288 (1998). https://doi.org/10.1007/BF02750393
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DOI: https://doi.org/10.1007/BF02750393