Summary: An estimator design problem is considered which involves both (least squares) and (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an state- estimation error criterion subject to a prespecified constraint on the state-estimation error. The 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 state-estimation error.
The principal result is a sufficient condition for characterizing fixed- order (i.e., full- and reduced-order) estimators with bounded and estimation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e., idempotent matrix. When the constraint is absent, the sufficient condition specializes to the state-estimation result given by the first author and D. C. Hyland [IEEE Trans. Autom. Control AC-30, 583-585 (1985; Zbl 0555.93056)].