This paper proposes a new model for a representation of linear system with delay. This latter, is given by decomposing the coefficients of the AutoRegressive with eXogenous input (ARX) model associated with the output and the input on two independent Meixner-like orthonormal bases. The resulting model is called ARX Meixner-like model. In order to ensure the parameter complexity reduction, the Meixner-like poles are optimized using Genetic algorithms method. Unknown But Bounded Error (UBBE) approaches are used to update the uncertainty domain of the parameters of the new obtained model. A numerical example of system with delay and two examples of experimental research are made to prove the efficiency of the proposed approach.
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