A combined invariant-subspace and subspace identification method for continuous-time state–space models using slowly sampled multi-sine-wave data

Abstract

The problem of identification of linear continuous-time (CT) state–space (SS) models directly from time-domain data is considered. Given multi-sine waves as excitation signals, this paper develops a new identification method called cISSIM (combined Invariant-Subspace and Subspace Identification Method), which is able to consistently identify CT SS models from slowly-sampled time-domain data in an error-in-variables framework. No prefiltering of the input/output signals is required which distinguishes cISSIM from other existing direct CT identification methods. Moreover, asymptotic unbiased estimates of the system state are obtained. A new persistence of excitation condition is also derived for cISSIM, which is shown to be related with the rank of a certain Khatri–Rao product.