Recursive identification of transfer function matrix in continuous systems via linear integral filter

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Abstract
A method is presented for identifying the transfer function matrix of a continuous-time multivariate system with unknown initial conditions from sampled data of input-output measurements. Using the so-called linear integral filter, an operation of numerical integration for handling time derivatives of measurements, leads to an identification model without involving the unknown initial conditions, and thus they do not require estimation together with the system parameters. Both a theoretical analysis and simulation study show that the least squares estimates are asymptotically biased even when the system outputs are corrupted by white noise. An instrumental variable method, where instrumental variables are composed of combinations of input signals, is proposed to give consistent estimates of system parameters for open-loop operation, and it is also thoroughly evaluated by Monte Carlo simulation analysis.