A Robust Strictly Passive Output-Error Identifier for Continuous-Time Systems
Résumé
This paper shows that the adaptive output error identifier for linear time--invariant continuous--time systems proposed by (cite{A. Betser}) is robust {em vis--'a--vis} measurement noise. More precisely, it is proven that the map from the noise to the estimation error is $mathcal{L}_2$--stable---provided a tuning parameter is chosen sufficiently large. A procedure to determine the required minimal value of this parameter is also given. If the noise is exponentially vanishing, asymptotic convergence to zero of the prediction error is achieved. Instrument for the establishment of the results is a suitable decomposition of the error system equations that allows us to strengthen---to {em strict}---the well--known passivity property of the identifier. The estimator does not require fast adaptation, a dead--zone, nor the knowledge of an upperbound on the noise magnitude, which is an essential requirement to prove stability of standard output error identifiers. To robustify the estimator with respect to non--square integrable (but bounded) noises a prediction error--dependent leakage term is added in the integral adaptation. A simulated example, which is unstable for the equation error identifier and the output error identifier of (cite{A. Betser}), is used to illustrate the noise insensitivity property of the new scheme.