Optimality of set-valued observers for linear systems

A guaranteed state estimator produces a set of possible states based on output measurements and models of exogenous signals. In this paper, the authors consider the guaranteed state estimation problem for linear time-varying systems with a priori magnitude bounds on exogenous signals. The authors provide a recursive algorithm to propagate the set of possible states based on output measurements. The authors show that the centers of these sets provide optimal estimates in an l^∞ -induced norm sense. The authors then consider the utility of guaranteed state estimators for disturbance rejection with output feedback. In particular, the authors derive a separation structure for disturbance rejection in the special case of output feedback with full control