Steady-state kalman filtering with an H∞ error bound

An estimator design problem is considered which involves both L₂ (least squares) and H_∞ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L₂ state-estimation error criterion subject to a prespecified H_∞ constraint on the state-estimation error. The H_∞ estimation-error constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on the L₂ state-estimation error. The principal result is a sufficient condition for characterizing fixed-order (i.e., full- and reduced-order) estimator with bounded L₂ and H_∞ estimation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e., idempotent matrix. When the H_∞ constraint is absent, the sufficient condition specializes to the L₂ state-estimation result given in [2]. The full version of this paper can be found in [10].