A robust output error identifier for continuous-time systems

This paper shows that the adaptive output error identifier for linear time-invariant continuous-time systems proposed by Bestser and Zeheb is robust vis-a-vis finite energy measurement noise. More precisely, it is proven that the map from the noise to the estimation error is L2-stableprovided 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. Instrumental for the establishment of the results is a suitable decomposition of the error system equations that allows us to strengthento strictthe well-known passivity property of the identifier. The estimator neither requires 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. L-stability of the modified scheme is established under a technical assumption. A simulated example, which is unstable for the equation error identifier and the output error identifier of Bestser and Zeheb, is used to illustrate the noise insensitivity property of the new scheme. Copyright (c) 2014 John Wiley & Sons, Ltd.