Identification of simple elements in Max-Algebra: Application to SISO discrete event systems modelisation

We propose to modelise the time behaviour of SISO discrete-event systems linear in Max-algebra. The method is inspired from the conventional linear system theory: from the impulse response, the model is obtained by using a decomposition of the system into a sum of first order sub-systems. From an ARMA form, we compute the parameters of the model by using both results of residuation theory to minimise an error criterion and decomposition of periodic series.