Three Approaches for System Identification by Impulse Response Fitting

Abstract

This paper addresses the problem of the identification of multivariable linear systems from measured or estimated samples of the impulse response. Most techniques are based on a low rank approximation of a block-Hankel matrix computed by a truncated singular value decomposition. The main drawback of such approaches is that the block-Hankel structure is not preserved in the approximation. Therefore these methods do not actually perform a term-wise fitting on the samples of the impulse response. Since the beginning of the 1990s, several algorithms were proposed for computing low rank approximations that maintain the matrix structure. But the methods available up until now still include limitations.In this article, three general and equivalent solutions to this identification problem are proposed in the general case of multiple-input multiple-output (MIMO) systems. They derive from a specific parametrization and perform a term-wise minimization of a least squares criterion on the samples of the impulse response.