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Steady-state Kalman filtering with an H error bound. (English) Zbl 0684.93081

Summary: An estimator design problem is considered which involves both L 2 (least squares) and H (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L 2 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 L 2 state-estimation error.

The principal result is a sufficient condition for characterizing fixed- order (i.e., full- and reduced-order) estimators with bounded L 2 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 L 2 state-estimation result given by the first author and D. C. Hyland [IEEE Trans. Autom. Control AC-30, 583-585 (1985; Zbl 0555.93056)].

93E11Filtering in stochastic control
46J15Banach algebras of differentiable or analytic functions, H p -spaces
15A24Matrix equations and identities