Une m\'ethode d'identification pour un syst\`eme lin\'eaire \`a retards

Abstract

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. $x''(t)+ax(t-h_{1})=bu(t-h_{2})$.