System Identification Based on Invariant Subspace

This article proposes a novel system identification method based on the notion of invariant subspace. It is shown that when the system input and output asymptotically converge onto an invariant subspace, a new form of regression can be obtained. New identification algorithms are then developed based on the obtained regression. The proposed method has several distinctive advantages originating from both time-domain and frequency-domain approaches. They include: 1) linear continuous-time models can be identified from slowly sampled input/output data; 2) consistency of the model parameters can be established in an error-in-variables framework; 3) the global optimum can be found by solving two linear least-square problems; and 4) the identification algorithms can be implemented online with explicit convergence rates. The theoretic results are tested by numerical examples to show the effectiveness of the proposed method.