Abstract
In this article, we explore the use of the Laguerre functions for the estimation of multivariable autoregressive with exogenous (ARX) input model. Each polynomial function of the MIMO ARX model associated to the inputs and to the outputs is expanded on independent Laguerre orthonormal bases. The resulting model is entitled MIMO ARX-Laguerre model. The optimal approximation of which is ensured once the poles characterising each Laguerre orthonormal basis are set to their optimal values. In this paper, a minimal recursive representation realisations for MIMO discrete-time linear systems are derived using Laguerre functions. Further we propose, from input/output measurements, an iterative optimisation algorithm for the free parameters (Laguerre poles). Simulation results show the effectiveness of the proposed optimal modelling method.
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