Analysis of Closed-loop Identification via the Joint Input-output Method and Stochastic Realization

Abstract

This paper studies closed-loop identification based on the joint input-output method and spectral density functions for finite data. It is well known that the spectral density function is given by stochastic subspace identification methods, where the finite interval stochastic realization is often used for analyzing and guaranteeing the positive realness. In this paper, it is shown how the finite-interval stochastic realization is used for closed loop identification, and moreover how the error due to the finiteness convergences to zero.