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

Abstract: 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.