  Recently, a novel system identification method based on invariant subspace
theory is introduced, aiming to address the identification problem of
continuous-time (CT) linear time-invariant (LTI) systems by combining
time-domain and frequency-domain methods. Subsequently, the combined
Invariant-Subspace and Subspace Identification Method (cISSIM) is introduced,
enabling direct estimation of CT LTI systems in state-space forms. It produces
consistent estimation that is robust in an error-in-variable and slow-sampling
conditions, while no pre-filtering operation of the input-output signals is
needed. This paper presents the discrete-cISSIM, which extends cISSIM to
discrete-time (DT) systems and offers the following improvements: 1) the
capability to utilize arbitrary discrete periodic excitations while cISSIM uses
multi-sine signals; 2) a faster estimation with reduced computational
complexity is proposed; 3) the covariance estimation problem can be addressed
concurrently with the system parameter estimation. An implementation of
discrete-cISSIM by MATLAB has also been provided.
