Sensitivity Penalization Based Robust State Estimation for Uncertain Linear Systems

This technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state-space model, based on a simultaneous minimization of nominal estimation errors and their sensitivities. An analytic solution is derived for the optimal estimator which can be recursively realized. This estimator has a form similar to the robust estimator of [6], and its computational complexity is comparable to the Kalman filter. Under certain conditions, this robust estimator is proved to converge to a stable system, its estimation errors have a bounded covariance matrix, and the estimate is asymptotically unbiased. Numerical simulations show that the obtained estimator has nice estimation performances.