Identification of fractional-order systems with both nonzero initial conditions and unknown time delays based on block pulse functions

In this paper, we present an effective method for the identification of fractional order system (FOS) with both nonzero initial conditions and unknown time delays based on a construction of suitable separable nonlinear least squares problem including both. The separable nonlinear least squares problem is first projected into the least squares problem only with respect to nonlinear parameters, time delays. Next, a bias compensated recursive least squares identification method is used to estimate the remaining linear parameters involving initial conditions of FOS. The effectiveness of the proposed method is illustrated by several simulations. •The identification method of fractional order systems with both nonzero initial conditions and unknown time delays.•Develop of a noble identification method based on block pulse functions.•Presentation of the explicit examples for showing the accuracy of the proposed method.