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In this paper, a method for multivariable discrete linear time-variant system identification is presented. This work is focused on slowly multivariable time-variant systems, so that it is possible to define time intervals, defined as windows, in which the system can be approximated by time-invariant models. In each window, a variation of N4SID that uses Markov parameters is applied and a state space model is estimated. For that reason the proposed method is defined as N4SID-VAR. After obtaining the models for all windows, the error between system model outputs are calculated and compared to the system outputs. The N4SID-VAR was tested with a time-variant multivariable benchmark and the results were accurate. The proposed method was also compared to the MOESP-VAR method and, for the tested benchmark, the N4SID-VAR was faster and more accurate than the MOESP-VAR algorithm.

N4SID-VAR Method for Multivariable Discrete Linear Time-variant System Identification