In this thesis, a presentation of a new canonical representation of multi-input multi-output systems is given. The new characterization covers the full range of practical situations in linear systems according to the structural properties and model of the perturbations which are known. Its direct link to ARMA processes as well as to classical state space representation ls also given.

The importance of the new representation lies in the fact that all unknown parameters and state variables appear linearly multiplied by either external variables (inputs and outputs) that appear in the data record, or by matrices that are only composed of zeroes and ones. This property enables us to perform a joint state and parameters estimation. Moreover, if the noises are gaussian and their statistics are known, an on-line algorithm that involves a standard discrete-time time-varying Kalman filter is proposed and used successfully in the estimation of unknown parameters for simulated examples.