According to the initial value problem in establishment of aero-engine small perturbation state variable model based on nonlinear fitting method

a linear fitting method against this problem was proposed.The objective function

in which the model outputs are linear functions of system matrix

was constructed by means of the known state sequences in discrete domain

resulting in transformation from nonlinear least square problem to linear least square problem.The method was applied to establish the small perturbation state variable model for a turbofan engine and then compared with nonlinear fitting method.The results show that its effectiveness not only avoids the initial value problem but also obtains better modeling precision.