A simple method for L2 approximation of unstable and nonminimum-phase systems

A simple performance-oriented method is proposed for approximation the unstable and nonminimum-phase systems. The performance index is taken to be a frequency-domain L₂-norm of the error between the step responses of the original and the reduced model. A frequency-domain weighted recursive least squares (RLS) algorithm is deduced and adopted to search for the optimal parameters of the approximation model. A numerical example is used to show the effectiveness of the proposed scheme. It is shown that the approximation models obtained by the proposed scheme yield zero steady-state gain errors and have the same RHP pole and RHP zero as the original system, resulting in well-matched dynamic behavior.