Abstract
In this paper we present the stationarity conditions for Laguerre and two-parameter Kautz models under a plethora of different conditions, viz., any combination ofi) continuous-time or discrete-time modelsii) impulsive (or white-noise) input signals or arbitrary input signalsiii) a time- or frequency-domain performance criterion based on an Lp, lp or an Hp 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 domainsv) 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 of the model 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.
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