Une méthode d'identification pour un système linéaire à retards

Details Une méthode d'identification pour un système linéaire à retards Une méthode d'identification pour un système linéaire à retards

2007-01-29

arxiv.org/abs/math/0701845v1

Mathematics

Optimization and Control

8 pages, 10 figures, 3 tables, extended version of a note submitted to the CRAS de Paris

Scientific paper

We provide a class of methods for the identification of a linear system with delay of the shape $x^{(n)}(t) = \sum_{i=0}^{n-1}a_{i}x^{(i)}(t) + bu(t-h)$. They allow the simultaneous identification of the parameters and delay, the observation of $x$ and its derivatives, knowing only generic input $u$ and output $x$. They are robust to the noise. Used in continuous time, they may follow the evolution of slowly varying parameters and noise. The method may be generalized to systems with two or more delays, e.g. $x''(t)+ax(t-h_{1})=bu(t-h_{2})$.

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