Interval Estimation for Continuous-time Linear Systems with Parametric Uncertainties
Résumé
This paper proposes a novel two-step intervalestimation method for continuous-time linear systems withparametric uncertainties. In the first step, a robust augmentedLuenberger-like observer with two observer gains is proposed.More formally, this state observer can be viewed as a cascadeof two estimators, where the second one is supplied by thedata provided by the first one. The first estimator is ableto attenuate the effect of the system uncertainty (uncertainparameters, process disturbance and measurement noise) on theaccuracy of the estimation error. Based on the output equationof the system, the second estimator improves the precision ofthe estimated state vector (provided by the first estimator) bysolving a Frobenius-norm optimization problem on the feasibledomain of the system output. In the second step, by allyingLyapunov stability theory with ellipsoidal analysis, guaranteedbounds on the estimation error are established. Throughouta numerical example, we show that the proposed approachoutperforms some existing methods in the literature.