Publication [6.17] of Tomás Oliveira e Silva

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Tomás Oliveira e Silva, "Optimal Pole Conditions for Laguerre and Two-Parameter Kautz Models: A Survey of Known Results," System Identification (SYSID 2000), vol. 2, pp. 457-462, 2000.


In this paper we present the stationarity conditions for Laguerre and two-parameter Kautz models under a plethora of different conditions, viz., any combination of i) continuous-time or discrete-time models, ii) impulsive (or white-noise) input signals or arbitrary input signals, iii) a time- or frequency domain performance criterion based on an L_p, \ell_p or an H_p norm, 1<p<∞, iv) existence, or not, of interpolation constraints in the response of the model to known signals, in the time- and/or frequency domains, v) utilization, or not, of a predefined set of fixed poles in the model. For Laguerre models, in all possible cases the optimality conditions take the same form, namely, either the last optimal weight vanishes or the last optimal weight of the model of the next higher order vanishes. For two-parameter Kautz models similar conditions hold, with the sole difference that the last two weights of the model vanish, instead of only a single weight. Unfortunately, these conditions are also satisfied in other stationarity points of the performance criterion.

BibTeX entry

  author = {Oliveira e Silva, Tom{\'a}s},
  title = {Optimal Pole Conditions for {L}aguerre and Two-Parameter {K}autz
          Models: A Survey of Known Results},
  booktitle = {System Identification (SYSID 2000)},
  year = {2000},
  editor = {Smith, Roy},
  volume = {2},
  pages = {457--462},
  publisher = {Pergamon}