Parametric Complexity Reduction of Discrete-Time Linear Systems Having a Slow Initial Onset or Delay

Abstract

This paper is concerned with an optimal expansion of linear discrete time systems on Meixner functions. Many orthogonal functions have been widely used to reduce the model parameter number such as Laguerre functions, Kautz functions and orthogonal basis functions. However, when the system has a slow initial onset or delay, Meixner functions, which have a slow start, are more suitable in terms of providing a more accurate approximation to the system. The optimal approximation of Meixner model is ensured once the pole characterizing the Meixner functions is set to its optimal value. In this paper, a new recursive representation of Meixner model is proposed. Further we propose, from input/output measurements, an iterative pole optimization algorithm of the Meixner pole functions. The method consists in applying the Newton-Raphson’s technique in which their elements are expressed analytically by using the derivative of the Meixner functions. Simulation results show the effectiveness of the proposed optimal modeling method.