A simple algorithm for stable order reduction of z-domain Laguerre models

Abstract

International audienceDiscrete-time Laguerre series are a well known and efficient tool in system identification and modeling. This paper presents a simple solution for stable and accurate order reduction of systems described by a Laguerre model

Unique condition for generalized Laguerre functions to solve pole position problem

“…We conducted a series of computational experiments presented in the form of three examples to support the theoretical results: the first two examples illustrate the problem solving results in the case of the continuous generalized Laguerre functions; the third example is provided to show the validity of the proposed results in the case of the discrete Laguerre functions considering the transfer function of a supersonic jet engine inlet described in [7].…”

“…In fact, this analytical solution has a major drawback concerned with the necessity for finding the roots of high-order polynomials, which can entail an enormous computational cost. This point, as a consequence, led to a substantial number of studies [2][3][4][5][6][7][8][9][10] into implicit, but improved methods to avoid the mentioned disadvantage. However, Clowes's explicit solution is still of considerable interest in signal processing applications.…”

Order reduction of Volterra and Volterra-Laguerre Models

“…The first order kernel of a Volterra system is a linear system and thus (6) is a classic approximation problem defined and solved in [8]. The process begins by defining a set of functions…”

“…Follows an iterative procedure analogous to (8) Follows the definition of the error terms to be minimized: The generalization to higher order kernels can easily be inferred when comparing (13) and (11). The method was purposefully designed to remain viable as the number of dimensions increases with each Volterra kernel.…”

“…It seeks to preserve all the advantages of Volterra models and all the recent results related to the latter while providing a bonus in terms of computational speed-up. It can be seen as a multilinear generalization of the method described in [8].…”