ANALYSIS OF STATE-SPACE SYSTEM-IDENTIFICATION METHODS BASED ON INSTRUMENTAL VARIABLES AND SUBSPACE FITTING

Subspace-based state-space system identification (4SID) methods have r ecently been proposed as an alternative to more traditional techniques for multivariable system identification. The advantages are that the user has simple and few design variables, and that the methods have ro bust numerical properties and relatively low computational complexitie s. Though subspace techniques have been demonstrated to perform well i n a number of cases, the performance of these methods is neither fully understood nor analyzed. Our principal objective is to undertake a st atistical investigation of subspace-based system identification techni ques. The studied methods consist of two steps. The subspace spanned b y the extended observability matrix is first estimated. The asymptotic properties of this subspace estimate are derived herein. In the secon d step, the structure of the extended observability matrix is used to find a system model estimate. Two possible methods are considered. The simplest one only uses a certain shift-invariance property, while in the other method a parametric representation of the null-space of the observability matrix is exploited. Explicit expressions for the asympt otic estimation error variances of the corresponding pole estimates ar e given. (C) 1997 Elsevier Science Ltd.