On Consistency of Subspace System Identification Methods

Abstract

System identification of linear dynamical systems using so-called subspace methods consists of two main steps, First, a signal subspace estimate is found. This usually corresponds to estimating the range space of the extended observability matrix. Then the system parameters are estimated from the subspace estimate. The main result of this note is explicit excitation conditions on the input signals, which guarantee consistent estimates of the range space of the extended observability matrix.