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Recently, a novel system identification method based on invariant subspacetheory is introduced, aiming to address the identification problem ofcontinuous-time (CT) linear time-invariant (LTI) systems by combiningtime-domain and frequency-domain methods. Subsequently, the combinedInvariant-Subspace and Subspace Identification Method (cISSIM) is introduced,enabling direct estimation of CT LTI systems in state-space forms. It producesconsistent estimation that is robust in an error-in-variable and slow-samplingconditions, while no pre-filtering operation of the input-output signals isneeded. This paper presents the discrete-cISSIM, which extends cISSIM todiscrete-time (DT) systems and offers the following improvements: 1) thecapability to utilize arbitrary discrete periodic excitations while cISSIM usesmulti-sine signals; 2) a faster estimation with reduced computationalcomplexity is proposed; 3) the covariance estimation problem can be addressedconcurrently with the system parameter estimation. An implementation ofdiscrete-cISSIM by MATLAB has also been provided.

Combined Invariant Subspace \& Frequency-Domain Subspace Method for Identification of Discrete-Time MIMO Linear Systems