Identification of a complete structured state space model

An advanced open-loop identification formulation is developed for linear stationary dynamical systems, including the model structure estimation. This approach is characterised by a mixed parameterisation using poles and polynomial coefficients for the zeros, especially designed to cope with parameter structure estimation (numbers of poles, zeros and delays). This choice offers the best possible precision for the dynamical parts of the system. Another property of the formulation concerns the minimisation of an output error criterion obtained by a non-linear optimisation in a reduced space dealing with the Lt non linear in the parameters Gt part of the model. Furthermore parameters bounding is sufficient to ensure dynamical stability. Unknown output offset and unknown initial conditions can be taken into account as supplementary ldquolinear in the parametersrdquo terms. Lastly, it is very easy to introduce some a priori knowledge (for instance, a pole exactly equal to 1, the knowledge of the static gain sign, etc.). In any case the parsimony principle is fully integrated in this approach and exploited through new validity parameters indicators in order to identify the model structure itself.