Identification of linear time-varying fractional order systems using block pulse functions based on repetitive principle.

A novel method for identifying linear time-varying fractional order systems based on a repetitive principle is proposed in this study. According to the repetitive principle, the system operates repetitively for several times, so the time-varying parameters are invariant on the fixed time for different operations. In the identification process, the time-varying parameters, independent from the input/output signals, are expanded onto some block pulse functions. The system is then converted to an algebraic system via the fractional differential operational matrix of the block pulse functions. Finally, recursive least square and instrumental variable recursive least square algorithms along the iteration axis are designed to identify the time-varying parameters without and with noise. Simulation results demonstrate that our proposed method is powerful in tracking time-varying parameters.