System approximations based on Meixner-like models

In this study, the authors investigate the parametric complexity reduction of the Meixner-like model for linear discrete-time system representation. The use of the Meixner-like functions is more suitable than the use of Laguerre functions and Kautz functions especially when the system have a slow initial onset or delay. The coefficients of the Meixner-like model can be estimated recursively from input–output data by the new representation. Noting that the selection of an arbitrary pole for the Meixner-like functions can raise the parameter number of the Meixner-like model. However, when the pole is set to its optimal value, an optimal expansion of transfer functions is produced. Therefore an optimisation technique is developed to generate the optimal Meixner-like pole, which is achieved by an iterative method, that consists in minimising the mean square error between the system output and the model output. Theoretical analysis and a numerical simulation show the efficiency of the approach.