Optimal pole conditions for Laguerre models that satisfy some interpolation constraints, using an || · ||p norm, 1 < p < ∞

The optimal pole conditions for Laguerre models are available in the literature for the || · ||₂ norms (for continuous-time or discrete-time systems, with or without an impulsive input signal, and in the time or frequency domains). Recently, the author was able to extend the available results i) to other || · ||_p norms, and ii) to models whose responses to known input signals satisfy, in the time and/or frequency domains, some interpolation constraints. In this paper we combine both extensions. It turns out that the optimality conditions for the poles of Laguerre models constrained as stated above, and using an || · ||_p norm, have the same functional form as the already available optimality conditions: the last optimal weight of the model vanishes or the last optimal weight of the model of the next higher order vanishes.